answers (lesson 10-1) - merrimack high school...1 3 x 1 8 the degree of a quadratic function is 2,...
TRANSCRIPT
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Gra
ph
ing
Qu
ad
rati
c F
un
cti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-1
10-1
©G
lencoe/M
cG
raw
-Hill
579
Gle
ncoe A
lgebra
1
Lesson 10-1
Gra
ph
Qu
ad
rati
c Fu
nct
ion
s
Qu
ad
rati
ca f
unction d
escribed b
y a
n e
quation o
f th
e f
orm
f(x
) 5
ax
21
bx
1c,
Exam
ple
:
Fu
ncti
on
where
aÞ
0y
52x
21
3x
18
Th
e d
egre
e o
f a q
uad
rati
c fu
nct
ion
is
2,an
d t
he e
xp
on
en
ts a
re p
osi
tive.G
rap
hs
of
qu
ad
rati
cfu
nct
ion
s h
ave a
gen
era
l sh
ap
e c
all
ed
a p
ara
bo
la.A
para
bola
op
en
s u
pw
ard
an
d h
as
am
inim
um
po
int
wh
en
th
e v
alu
e o
f a
is p
osi
tive,an
d a
para
bola
op
en
s d
ow
nw
ard
an
d h
as
am
ax
imu
m p
oin
tw
hen
th
e v
alu
e o
f a
is n
egati
ve.
Use a
ta
ble
of
va
lues t
o
gra
ph
y5
x2
24x
11.
Gra
ph
th
e o
rdere
d p
air
s in
th
e t
able
an
dco
nn
ect
th
em
wit
h a
sm
ooth
cu
rve.x
y
O
xy
21
6
01
12
2
22
3
32
2
41
Use a
ta
ble
of
va
lues t
o
gra
ph
y5
2x
22
6x
27.
Gra
ph
th
e o
rdere
d p
air
s in
th
e t
able
an
dco
nn
ect
th
em
wit
h a
sm
ooth
cu
rve.
x
y
O
xy
26
27
25
22
24
1
23
2
22
1
21
22
02
7
Example
1Example
1Example
2Example
2
Exercises
Exercises
Use a
ta
ble
of
va
lues t
o g
ra
ph
ea
ch
fu
ncti
on
.
1.
y5
x2
12
2.
y5
2x
22
43.
y5
x2
23
x1
2
x
y
O
x
y
O
x
y
O
©G
lencoe/M
cG
raw
-Hill
580
Gle
ncoe A
lgebra
1
Sym
metr
y a
nd
Vert
ices
Para
bola
s h
ave a
geom
etr
ic p
rop
ert
y c
all
ed
sy
mm
etr
y.T
hat
is,if
th
e f
igu
re i
s fo
lded
in
half
,each
half
wil
l m
atc
h t
he o
ther
half
exact
ly.T
he v
ert
ical
lin
eco
nta
inin
g t
he f
old
lin
e i
s ca
lled
th
e a
xis
of
sy
mm
etr
y.
Axis
of
For
the p
ara
bola
y5
ax
21
bx
1c,
where
aÞ
0,
Exam
ple
:T
he a
xis
of
sym
metr
y o
f
Sym
metr
yth
e lin
e x
52
is t
he a
xis
of
sym
metr
y.y
5x
21
2x
15 is t
he lin
e x
52
1.
Th
e a
xis
of
sym
metr
y c
on
tain
s th
e m
inim
um
or
maxim
um
poin
t of
the p
ara
bola
,th
e v
erte
x.
Co
nsid
er t
he g
ra
ph
of
y5
2x
21
4x
11.
b} 2
a
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Gra
ph
ing
Qu
ad
rati
c F
un
cti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-1
10-1
Example
Example
a.
Writ
e t
he e
qu
ati
on
of
the a
xis
of
sy
mm
etr
y.
In y
52
x2
14
x1
1,a
52 a
nd
b5
4.
Su
bst
itu
te t
hese
valu
es
into
th
e e
qu
ati
on
of
the a
xis
of
sym
metr
y.
x5
2
x5
25
21
Th
e a
xis
of
sym
metr
y i
s x
52
1.
4} 2
(2)
b} 2
a
b.
Fin
d t
he c
oo
rd
ina
tes o
f th
e v
erte
x.
Sin
ce t
he e
qu
ati
on
of
the a
xis
of
sym
metr
y i
s x
52
1 a
nd
th
e v
ert
ex l
ies
on
th
e a
xis
,th
e x
-coord
inate
of
the v
ert
ex
is 2
1.
y5
2x
21
4x
11
Origin
al equation
y5
2(2
1)2
14(2
1)
11
Substitu
te.
y5
2(1
) 2
4 1
1S
implif
y.
y5
21
Th
e v
ert
ex i
s at
(21,
21).
c.
Iden
tify
th
e v
erte
x a
s a
ma
xim
um
or
a m
inim
um
.
Sin
ce t
he c
oeff
icie
nt
of
the x
2-t
erm
is
posi
tive,th
e p
ara
bola
op
en
s u
pw
ard
,an
dth
e v
ert
ex i
s a m
inim
um
poin
t.
d.
Gra
ph
th
e f
un
cti
on
.
x
y O
( –1, –1)
x 5
–1
Exercises
Exercises
Writ
e t
he e
qu
ati
on
of
the a
xis
of
sy
mm
etr
y,
an
d f
ind
th
e c
oo
rd
ina
tes o
f th
e v
erte
x
of
the g
ra
ph
of
ea
ch
fu
ncti
on
.Id
en
tify
th
e v
erte
x a
s a
ma
xim
um
or a
min
imu
m.
Th
en
gra
ph
th
e f
un
cti
on
.
1.
y5
x2
13
2.
y5
2x
22
4x
24
3.
y5
x2
12
x1
3
x5
0;
(0,3);
min
x5
22;
(22,0);
max
x5
21;
(21,2);
min
x
y
O
x
y
O
x
y
O
Answers (Lesson 10-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
Gra
ph
ing
Qu
ad
rati
c F
un
cti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-1
10-1
©G
lencoe/M
cG
raw
-Hill
581
Gle
ncoe A
lgebra
1
Lesson 10-1
Use a
ta
ble
of
va
lues t
o g
ra
ph
ea
ch
fu
ncti
on
.
1.
y5
x2
24
2.
y5
2x
21
3
3.
y5
x2
22
x2
64.
y5
2x
22
4x
11
Writ
e t
he e
qu
ati
on
of
the a
xis
of
sy
mm
etr
y,
an
d f
ind
th
e c
oo
rd
ina
tes o
f th
e v
erte
x
of
the g
ra
ph
of
ea
ch
fu
ncti
on
.Id
en
tify
th
e v
erte
x a
s a
ma
xim
um
or m
inim
um
.
Th
en
gra
ph
th
e f
un
cti
on
.
5.
y5
2x
26.
y5
x2
22
x2
57.
y5
2x
21
4x
21
x5
0;
(0,0);
min
x5
1;
(1,
26);
min
x5
2;
(2,3);
max
8.
y5
2x
22
2x
12
9.
y5
2x
21
4x
22
10.
y5
22
x2
24x
16
x5
21;
(21,3);
max
x5
21;
(21,
24);
min
x5
21;
(21,8);
max
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
©G
lencoe/M
cG
raw
-Hill
582
Gle
ncoe A
lgebra
1
Use a
ta
ble
of
va
lues t
o g
ra
ph
ea
ch
fu
ncti
on
.
1.
y5
2x
21
22.
y5
x2
26
x1
33.
y5
22x
22
8x
25
Writ
e t
he e
qu
ati
on
of
the a
xis
of
sy
mm
etr
y,
an
d f
ind
th
e c
oo
rd
ina
tes o
f th
e v
erte
x
of
the g
ra
ph
of
ea
ch
fu
ncti
on
.Id
en
tify
th
e v
erte
x a
s a
ma
xim
um
or m
inim
um
.
Th
en
gra
ph
th
e f
un
cti
on
.
4.
y5
2x
21
35.
y5
22x
21
8x
23
6.
y5
2x
21
8x
11
x5
0;
(0,3);
max
x5
2;
(2,5);
max
x5
22;
(22,
27);
min
PH
YS
ICS
Fo
r E
xercis
es 7
–9,
use t
he f
oll
ow
ing
in
form
ati
on
.
Mir
an
da t
hro
ws
a s
et
of
keys
up
to h
er
bro
ther,
wh
o i
s st
an
din
g o
n a
th
ird
-sto
ry b
alc
on
yw
ith
his
han
ds
38 f
eet
above t
he g
rou
nd
.If
Mir
an
da t
hro
ws
the k
eys
wit
h a
n i
nit
ial
velo
city
of
40 f
eet
per
seco
nd
,th
e e
qu
ati
on
h5
216t2
140t
15 g
ives
the h
eig
ht
hof
the k
eys
aft
er
tse
con
ds.
7.
How
lon
g d
oes
it t
ak
e t
he k
eys
to r
each
th
eir
hig
hest
poin
t?1.2
5 s
8.
How
hig
h d
o t
he k
eys
reach
?30 f
t
9.
Wil
l h
er
bro
ther
be a
ble
to c
atc
h t
he k
eys?
Exp
lain
.N
o,th
e k
eys w
ill
be 8
ft
sh
ort
of
their
targ
et.
BA
SE
BA
LL
Fo
r E
xercis
es 1
0–12,
use t
he f
oll
ow
ing
in
form
ati
on
.
A p
layer
hit
s a b
ase
ball
at
a 4
5°
an
gle
wit
h t
he g
rou
nd
wit
h a
n i
nit
ial
velo
city
of
80 f
eet
per
seco
nd
fro
m a
heig
ht
of
thre
e f
eet
above t
he g
rou
nd
.T
he e
qu
ati
on
h5
20.0
05x
21
x1
3 g
ives
the p
ath
of
the b
all
,w
here
his
th
e h
eig
ht
an
d x
is t
he h
ori
zon
tal
dis
tan
ce t
he b
all
tra
vels
.
10.W
hat
is t
he e
qu
ati
on
of
the a
xis
of
sym
metr
y?
x5
10
0
11.W
hat
is t
he m
axim
um
heig
ht
reach
ed
by t
he b
ase
ball
?53 f
t
12.A
n o
utf
ield
er
catc
hes
the b
all
th
ree f
eet
above t
he g
rou
nd
.H
ow
far
has
the b
all
tra
vele
dh
ori
zon
tall
y w
hen
th
e o
utf
ield
er
catc
hes
it?
200 f
t
x
y
O
x
y
O
x
y
O
x
y O
x
y
Ox
y
OPra
cti
ce (
Avera
ge)
Gra
ph
ing
Qu
ad
rati
c F
un
cti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-1
10-1
Answers (Lesson 10-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
Gra
ph
ing
Qu
ad
rati
c F
un
cti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-1
10-1
©G
lencoe/M
cG
raw
-Hill
583
Gle
ncoe A
lgebra
1
Lesson 10-1
Pre
-Act
ivit
yH
ow
ca
n y
ou
co
ord
ina
te a
fir
ew
ork
s d
isp
lay
wit
h r
eco
rd
ed
mu
sic?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
0-1
at
the
top
of
page
524 i
n y
our
textb
ook
.
Acc
ord
ing t
o th
e gra
ph
,at
wh
at
hei
gh
t d
oes
the
rock
et e
xp
lod
e an
d i
n h
owm
an
y s
econ
ds
aft
er b
ein
g l
au
nch
ed?
It e
xp
lod
es a
t a h
eig
ht
of
80 m
ete
rs 4
seco
nd
s a
fter
bein
g l
au
nch
ed
.
Read
ing
th
e L
ess
on
1.
Th
e st
an
dard
for
m f
or a
fu
nct
ion
is
y5
ax
21
bx
1c.
For
th
e
fun
ctio
n y
52
x2
25
x1
3,th
e valu
e of
ais
,th
e valu
e of
bis
,an
d
the
valu
e of
cis
.
2.
Th
e gra
ph
s of
tw
o qu
ad
rati
c fu
nct
ion
s are
sh
own
bel
ow.C
omp
lete
each
sta
tem
ent
abou
tth
e gra
ph
s.
A.
B.
a.
Each
gra
ph
is
a c
urv
e ca
lled
a
.
b.
Th
e h
igh
est
poi
nt
of g
rap
h A
is
loca
ted
at
.T
his
poi
nt
is t
he
(maxim
um
/min
imu
m)
poi
nt
of t
he
gra
ph
.
c.
Th
e lo
wes
t p
oin
t of
gra
ph
B i
s lo
cate
d a
t .T
his
poi
nt
is t
he
(maxim
um
/min
imu
m)
poi
nt
of t
he
gra
ph
.
3.
Th
e m
axim
um
or
min
imu
m p
oin
t of
a p
ara
bol
a i
s ca
lled
th
e of
th
e p
ara
bol
a.
4.
If y
ou f
old
a p
ara
bol
a a
lon
g a
lin
e to
get
tw
o h
alv
es t
hat
matc
h e
xact
ly,th
e li
ne
wh
ere
you
fol
d t
he
para
bol
a i
s th
e of
th
e p
ara
bol
a.T
his
lin
e goe
s
thro
ugh
th
e of
th
e p
ara
bol
a.
5.
For
a q
uad
rati
c fu
nct
ion
y5
ax
21
bx
1c,
the
para
bol
a o
pen
s u
pw
ard
if
a0.
It o
pen
s d
own
ward
if
a0.
Help
ing
Yo
u R
em
em
ber
6.
Loo
k u
p t
he
wor
d v
erte
xin
a d
icti
onary
.Y
ou w
ill
fin
d t
hat
it c
omes
fro
m t
he
Lati
n w
ord
ver
tere
,w
hic
h m
ean
s to
tu
rn.H
ow c
an
you
use
th
e id
ea o
f “t
o tu
rn”
to r
emem
ber
wh
at
the
ver
tex o
f a p
ara
bol
a i
s?S
am
ple
an
sw
er:
Th
e v
ert
ex o
f a p
ara
bo
la i
s t
he
po
int
at
wh
ich
th
e p
ara
bo
la t
urn
s u
pw
ard
or
do
wn
ward
.
,
.
vert
ex
axis
of
sym
metr
y
vert
ex
min
imu
m
(21,
22)
ma
xim
um
(21,4)
para
bo
la
x
y
O
x
y
O
3
25
2
qu
ad
rati
c
©G
lencoe/M
cG
raw
-Hill
584
Gle
ncoe A
lgebra
1
Tra
nsla
tin
g Q
uad
rati
c G
rap
hs
Wh
en a
fig
ure
is
mov
ed t
o a n
ew p
osit
ion
wit
hou
t u
nd
ergoi
ng a
ny r
otati
on,th
en t
he
figu
re i
s sa
id t
o h
ave
bee
n t
ran
sla
ted
to t
hat
pos
itio
n.
Th
e gra
ph
of
a q
uad
rati
c eq
uati
on i
n t
he
form
y
5(x
2b)2
1c
is a
tra
nsl
ati
on o
f th
e gra
ph
of
y5
x2.
Sta
rt w
ith
y5
x2.
Sli
de
to t
he
righ
t 4 u
nit
s.
y5
(x2
4)2
Th
en s
lid
e u
p 3
un
its.
y5
(x2
4)2
13
Th
ese
eq
ua
tio
ns
ha
ve t
he f
orm
y5
x2
1c.
Gra
ph
ea
ch
eq
ua
tio
n.
1.
y5
x2
11
2.
y5
x2
12
3.
y5
x2
22
Th
ese
eq
ua
tio
ns
ha
ve t
he f
orm
y5
(x2
b)2
.G
ra
ph
ea
ch
eq
ua
tio
n.
4.
y5
(x2
1)2
5.
y5
(x2
3)2
6.
y5
(x1
2)2
x
y Ox
y Ox
y O
x
y Ox
y Ox
y O
x
y O
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-1
10-1
Answers (Lesson 10-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y G
rap
hin
g
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-2
10-2
©G
lencoe/M
cG
raw
-Hill
585
Gle
ncoe A
lgebra
1
Lesson 10-2
So
lve b
y G
rap
hin
g
Qu
ad
rati
c E
qu
ati
on
an e
quation o
f th
e f
orm
ax
21
bx
1c
50,
where
aÞ
0
Th
e so
luti
ons
of a
qu
ad
rati
c eq
uati
on a
re c
all
ed t
he
roo
tsof
th
e eq
uati
on.T
he
root
s of
a q
uad
rati
c eq
uati
on c
an
be
fou
nd
by g
rap
hin
g t
he
rela
ted
qu
ad
rati
c fu
nct
ion
f(
x)
5a
x2
1bx
1c
an
d f
ind
ing t
he
x-i
nte
rcep
ts o
r zero
sof
th
e fu
nct
ion
.
So
lve x
21
4x
13 5
0 b
yg
ra
ph
ing
.
Gra
ph
th
e re
late
d f
un
ctio
n f
(x)
5x
21
4x
13.
Th
e eq
uati
on o
f th
e axis
of
sym
met
ry i
s
x5
2or
22.T
he
ver
tex i
s at
( 2
2,
21).
Gra
ph
th
e ver
tex a
nd
sev
eral
oth
er p
oin
ts o
nei
ther
sid
e of
th
e axis
of
sym
met
ry.
To
solv
e x
21
4x
13 5
0,you
nee
d t
o k
now
wh
ere
the
valu
e of
f(x
) 5
0.T
his
occ
urs
at
the
x-i
nte
rcep
ts,
23 a
nd
21.
Th
e so
luti
ons
are
23 a
nd
21.
xO
f(x)
4} 2
(1)
So
lve x
22
6x
19 5
0 b
yg
ra
ph
ing
.
Gra
ph
th
e re
late
d f
un
ctio
n f
(x)
5x
22
6x
19.
Th
e eq
uati
on o
f th
e axis
of
sym
met
ry i
s
x5
or 3
.T
he
ver
tex i
s at
( 3,0).
Gra
ph
the
ver
tex a
nd
sev
eral
oth
er p
oin
ts o
n e
ith
ersi
de
of t
he
axis
of
sym
met
ry.
To
solv
e x
22
6x
19 5
0,you
nee
d t
o k
now
wh
ere
the
valu
e of
f(x
) 5
0.T
he
ver
tex o
f th
ep
ara
bol
a i
s th
e x-i
nte
rcep
t.T
hu
s,th
e on
lyso
luti
on i
s 3.
x
f(x) O
6} 2
(1)
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n b
y g
ra
ph
ing
.
1.
x2
17x
112 5
02.
x2
2x
212 5
03.
x2
24
x1
5 5
0
23;
24
4,
23
no
real
roo
ts
x
f (x)
O
x
f (x)
O4
4
24
28
212
82
42
8
x
f (x)
O
©G
lencoe/M
cG
raw
-Hill
586
Gle
ncoe A
lgebra
1
Est
imate
So
luti
on
sT
he
root
s of
a q
uad
rati
c eq
uati
on m
ay n
ot b
e in
teger
s.If
exact
root
s ca
nn
ot b
e fo
un
d,th
ey c
an
be
esti
mate
d b
y f
ind
ing t
he
con
secu
tive
inte
ger
s bet
wee
nw
hic
h t
he
root
s li
e. So
lve x
21
6x
16 5
0 b
y g
ra
ph
ing
.If
in
teg
ra
l ro
ots
ca
nn
ot
be f
ou
nd
,est
ima
te t
he r
oo
ts b
y s
tati
ng
th
e c
on
secu
tiv
e i
nte
gers
betw
een
wh
ich
th
e r
oo
ts l
ie.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y G
rap
hin
g
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-2
10-2
Example
Example
Gra
ph
th
e re
late
d f
un
ctio
n f
(x)
5x
21
6x
16.
Not
ice
that
the
valu
e of
th
e fu
nct
ion
ch
an
ges
fr
om n
egati
ve
to p
osit
ive
bet
wee
n t
he
x-v
alu
es
of 2
5 a
nd
24 a
nd
bet
wee
n 2
2 a
nd
21.
xf(
x)
25
1
24
22
23
23
22
22
21
1
x
f(x)
O
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n b
y g
ra
ph
ing
.If
in
teg
ra
l ro
ots
ca
nn
ot
be f
ou
nd
,est
ima
te t
he
ro
ots
by
sta
tin
g t
he c
on
secu
tiv
e i
nte
gers
betw
een
wh
ich
th
e r
oo
ts l
ie.
1.
x2
17x
19 5
02.
x2
2x
24 5
03.
x2
24x
16 5
0
26 ,
x,
25,
22 ,
x,
21,
no
real
roo
ts2
2 ,
x,
21
2 ,
x,
3
4.
x2
24x
21 5
05.
4x
22
12x
13 5
06.
x2
22x
24 5
0
21 ,
x,
0,
0 ,
x,
1,
22 ,
x,
21,
4 ,
x,
52 ,
x,
33 ,
x,
4
x
f (x)
O
x
f (x)
O
x
f (x)
O
x
f (x)
O
x
f (x)
O
x
f (x)
O
Th
e x-i
nte
rcep
ts o
f th
e gra
ph
are
bet
wee
n 2
5 a
nd
24 a
nd
bet
wee
n 2
2 a
nd
21.
So
one
root
is
bet
wee
n 2
5 a
nd
24,an
d t
he
oth
er r
oot
is b
etw
een
22 a
nd
21.
Answers (Lesson 10-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
racti
ce
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y G
rap
hin
g
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-2
10-2
©G
lencoe/M
cG
raw
-Hill
587
Gle
ncoe A
lgebra
1
Lesson 10-2
So
lve e
ach
eq
ua
tio
n b
y g
ra
ph
ing
.
1.
x2
24x
15 5
0[
2.
c21
6c
18 5
02
4,
22
3.
a2
22a
52
11
4.
n2
27
n5
210
2,5
So
lve e
ach
eq
ua
tio
n b
y g
ra
ph
ing
.If
in
teg
ra
l ro
ots
ca
nn
ot
be f
ou
nd
,est
ima
te t
he
ro
ots
by
sta
tin
g t
he c
on
secu
tiv
e i
nte
gers
betw
een
wh
ich
th
e r
oo
ts l
ie.
5.
p2
14p
12 5
06.
x2
1x
23 5
0
24 ,
p,
23,
21 ,
p,
02
3 ,
x,
22,1 ,
x,
2
7.
d2
16
d5
23
8.
h2
11 5
4h
26 ,
d,
25,
21 ,
d,
00 ,
h,
1,3 ,
h,
4
hO
f(h)
dO
f(d
)
xO
f(x)
pO
f(p)
nO
f(n)
a
f (a)
O
cO
f(c)
xO
f(x)
©G
lencoe/M
cG
raw
-Hill
588
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n b
y g
ra
ph
ing
.
1.
x2
25x
16 5
02,3
2.
w2
16
w1
9 5
02
33.
b2
24
b1
5 5
0[
So
lve e
ach
eq
ua
tio
n b
y g
ra
ph
ing
.If
in
teg
ra
l ro
ots
ca
nn
ot
be f
ou
nd
,est
ima
te t
he
ro
ots
by
sta
tin
g t
he c
on
secu
tiv
e i
nte
gers
betw
een
wh
ich
th
e r
oo
ts l
ie.
4.
p2
14p
53
5.
2m
21
5 5
10m
6.
2v
21
8v
52
7
25 ,
p,
24,
0 ,
m,
1,
23 ,
v,
22,
0 ,
p,
14 ,
m,
52
2 ,
v,
21
NU
MB
ER
TH
EO
RY
Fo
r E
xercis
es
7 a
nd
8,
use
th
e
foll
ow
ing
in
form
ati
on
.
Tw
o n
um
ber
s h
ave
a s
um
of
2 a
nd
a p
rod
uct
of
28.T
he
qu
ad
rati
c eq
uati
on 2
n2
12n
18 5
0 c
an
be
use
d t
o d
eter
min
e th
e tw
o n
um
ber
s.
7.
Gra
ph
th
e re
late
d f
un
ctio
n f
(n)
52
n2
12n
18 a
nd
d
eter
min
e it
s x-i
nte
rcep
ts.
22,4
8.
Wh
at
are
th
e tw
o n
um
ber
s?2
2 a
nd
4
DE
SIG
NF
or E
xercis
es
9 a
nd
10,
use
th
e f
oll
ow
ing
in
form
ati
on
.
A f
ootb
rid
ge
is s
usp
end
ed f
rom
a p
ara
bol
ic s
up
por
t.T
he
fun
ctio
n
h(x
) 5
2x
21
9 r
epre
sen
ts t
he
hei
gh
t in
fee
t of
th
e su
pp
ort
abov
e
the
walk
way,
wh
ere
x5
0 r
epre
sen
ts t
he
mid
poi
nt
of t
he
bri
dge.
9.
Gra
ph
th
e fu
nct
ion
an
d d
eter
min
e it
s x-i
nte
rcep
ts.
215,15
10.W
hat
is t
he
len
gth
of
the
walk
way b
etw
een
th
e tw
o su
pp
orts
?30 f
t
1} 2
5x
h (x)
O6
12
12 6
26
212
212
26
n
f (n)
O
v
f(v)
O
m
f (m
)
Op
O
f(p)
b
f (b)
O
w
f (w
)
Ox
O
f(x)Pra
cti
ce (
Avera
ge)
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y G
rap
hin
g
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-2
10-2
Answers (Lesson 10-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y G
rap
hin
g
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-2
10-2
©G
lencoe/M
cG
raw
-Hill
589
Gle
ncoe A
lgebra
1
Lesson 10-2
Pre
-Act
ivit
yH
ow
ca
n q
ua
dra
tic e
qu
ati
on
s b
e u
sed
in
co
mp
ute
r s
imu
lati
on
s?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
0-2
at
the
top
of
page
533 i
n y
our
textb
ook
.
If o
ne
of t
he
x-i
nte
rcep
ts r
epre
sen
ts t
he
loca
tion
wh
ere
the
ball
wil
l h
it t
he
gro
un
d,w
hat
doe
s th
e ot
her
x-i
nte
rcep
t re
pre
sen
t?T
he l
ocati
on
wh
ere
the b
all i
s h
it.
Read
ing
th
e L
ess
on
1.
Th
e x-i
nte
rcep
ts o
f th
e gra
ph
of
a q
uad
rati
c fu
nct
ion
are
th
e x-c
oord
inate
s of
th
e p
oin
tsw
her
e th
e gra
ph
of
the
fun
ctio
n i
nte
rsec
ts t
he
x-a
xis
.A
t th
ose
poi
nts
,th
e y-c
oord
inate
s
are
equ
al
to
.T
his
exp
lain
s w
hy t
he
x-i
nte
rcep
ts a
re c
all
ed
of t
he
qu
ad
rati
c fu
nct
ion
.
2.
Th
e gra
ph
s of
th
ree
fun
ctio
ns
are
sh
own
bel
ow.U
se t
he
gra
ph
s to
pro
vid
e th
e re
qu
este
din
form
ati
on a
bou
t th
e re
late
d q
uad
rati
c eq
uati
ons.
A.
f(x)
5x
22
6x
19
B.
f(x)
5x
21
2x
13
C.
f(x)
5x
21
x2
2
a.
For
Gra
ph
A,th
e re
late
d q
uad
rati
c eq
uati
on i
s .
How
man
y s
olu
tion
s are
th
ere?
on
e
Nam
e an
y s
olu
tion
s.3
b.
For
Gra
ph
B,th
e re
late
d q
uad
rati
c eq
uati
on i
s .
How
man
y s
olu
tion
s are
th
ere?
no
ne
Nam
e an
y s
olu
tion
s.n
on
e
c.
For
Gra
ph
C,th
e re
late
d q
uad
rati
c eq
uati
on i
s .
How
man
y s
olu
tion
s are
th
ere?
two
Nam
e an
y s
olu
tion
s.2
2 a
nd
1
Help
ing
Yo
u R
em
em
ber
3.
Des
crib
e h
ow y
ou c
an
rem
ember
th
at
the
wor
d z
ero
is u
sed
wh
en y
ou a
re t
alk
ing a
bou
tfu
nct
ion
s,bu
t th
e w
ord
root
is u
sed
wh
en y
ou a
re t
alk
ing a
bou
t eq
uati
ons.
Sam
ple
an
sw
er:
So
me f
un
cti
on
s c
an
have a
valu
e o
f zero
.E
qu
ati
on
s c
an
be t
rue
or
fals
e,b
ut
they d
o n
ot
have a
nu
mb
er
valu
e.x
21
x2
2 5
0
x2
12
x1
3 5
0
x2
26
x1
9 5
0
xO
f(x)
xO
f(x)
xO
f(x)
ze
ros
0
©G
lencoe/M
cG
raw
-Hill
590
Gle
ncoe A
lgebra
1
Od
d N
um
bers
an
d P
ara
bo
las
Th
e so
lid
para
bol
a a
nd
th
e d
ash
ed s
tair
-ste
p g
rap
h a
re
rela
ted
.T
he
para
bol
a i
nte
rsec
ts t
he
stair
ste
ps
at
thei
r in
sid
e co
rner
s.
Use
th
e f
igu
re f
or E
xercis
es
1–3.
1.
Wh
at
is t
he
equ
ati
on o
f th
e p
ara
bol
a?
y5
x2
2.
Des
crib
e th
e h
oriz
onta
l se
ctio
ns
of t
he
stair
-ste
p g
rap
h.
Each
is 1
un
it w
ide
.
3.
Des
crib
e th
e ver
tica
l se
ctio
ns
of t
he
stair
-ste
p g
rap
h.
Th
ey f
orm
th
e s
eq
uen
ce 1
,3,5,7.
Use
th
e s
eco
nd
fig
ure f
or E
xercis
es
4–6.
4.
Wh
at
is t
he
equ
ati
on o
f th
e p
ara
bol
a?
y5
x2
5.
Des
crib
e th
e h
oriz
onta
l se
ctio
ns
of t
he
stair
ste
ps.
Each
is 1
un
it w
ide
.
6.
Des
crib
e th
e ver
tica
l se
ctio
ns.
Th
ey f
orm
th
e s
eq
uen
ce
,,
,,
.
7.
How
doe
s th
e gra
ph
of
y5
x2
rela
te t
o th
e se
qu
ence
of
nu
mber
s ,
,,
,…
?
If t
he x
valu
es i
ncre
ase b
y 1
,th
e y
valu
es i
ncre
ase b
y t
he n
um
bers
in
th
e s
eq
uen
ce
.
8.
Com
ple
te t
his
con
clu
sion
.T
o gra
ph
a p
ara
bol
a w
ith
th
e eq
uati
on y
5a
x2,st
art
at
the
ver
tex.T
hen
go
over
1 a
nd
up
a;ov
er 1
an
d u
p 3
a;
over
1 a
nd
up
5a;
over
1 a
nd
up
7a
;an
d s
o o
n.T
he c
oeff
icie
nts
of
aare
the o
dd
nu
mb
ers
.
7 } 2
5 } 2
3 } 2
1 } 2
1 } 2
9 } 27 } 2
5 } 23 } 2
1 } 2
1 } 2
x
y O
x
y O
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-2
10-2
Answers (Lesson 10-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y C
om
ple
tin
g t
he S
qu
are
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-3
10-3
©G
lencoe/M
cG
raw
-Hill
591
Gle
ncoe A
lgebra
1
Lesson 10-3
Fin
d t
he S
qu
are
Ro
ot
An
equ
ati
on s
uch
as
x2
24x
14 5
5 c
an
be
solv
ed b
y t
ak
ing
the
squ
are
roo
t of
each
sid
e.
So
lve x
22
2x
11 5
9.
Ro
un
d t
o t
he n
ea
rest
ten
th i
fn
ecess
ary.
x2
22
x1
1 5
9
(x2
1)2
59
Ï(x
21
w)2 w
5Ï
9w|x
21
|5Ï
9wx
21 5
63
x2
1 1
1 5
63 1
1
x5
1 6
3
x5
1 1
3or
x5
1 2
3
54
52
2
Th
e so
luti
on s
et i
s {2
2,4}.
So
lve x
22
4x
14 5
5.
Ro
un
d t
o t
he n
ea
rest
ten
th i
fn
ecess
ary.
x2
24x
14 5
5
(x2
2)2
55
Ï(x
22
w)2 w
5Ï
5w|x
22
|5
Ï5w
x2
2 5
6Ï
5wx
22 1
2 5
6Ï
5w1
2
x5
2 6
Ï5w
Use
a c
alc
ula
tor
to e
valu
ate
each
valu
e of
x.
x5
2 1
Ï5w
orx
52 2
Ï5w
<4.2
<2
0.2
Th
e so
luti
on s
et i
s {2
0.2
,4.2
}.
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n b
y t
ak
ing
th
e s
qu
are r
oo
t o
f ea
ch
sid
e.
Ro
un
d t
o t
he n
ea
rest
ten
th i
f n
ecess
ary.
1.
x2
14x
14 5
92.
m2
112m
136 5
13.
r22
6r
19 5
16
25,1
27,
25
21,7
4.
x2
22x
11 5
25
5.
x2
28
x1
16 5
56.
x2
210x
125 5
8
24,6
1.8
,6.2
2.2
,7.8
7.
c22
4c
14 5
78.
p2
116p
164 5
39.
x2
18
x1
16 5
9
20.6
,4.6
29.7
,2
6.3
27,
21
10.x
21
6x
19 5
411.
a2
18a
116 5
10
12.
y2
212y
136 5
5
25,
21
27.2
,2
0.8
3.8
,8.2
13.x
21
10x
125 5
114.
y2
114y
149 5
615.
m2
28m
116 5
2
26,
24
29.4
,2
4.6
2.6
,5.4
16.x
21
12x
136 5
10
17.
a2
214a
149 5
318.
y2
18
y1
16 5
7
29.2
,2
2.8
5.3
,8.7
26.6
,2
1.4
©G
lencoe/M
cG
raw
-Hill
592
Gle
ncoe A
lgebra
1
Co
mp
lete
th
e S
qu
are
Sin
ce f
ew q
uad
rati
c ex
pre
ssio
ns
are
per
fect
squ
are
tri
nom
ials
,th
e m
eth
od o
f co
mp
leti
ng
th
e s
qu
are
can
be
use
d t
o so
lve
som
e qu
ad
rati
c eq
uati
ons.
Use
the
foll
owin
g s
tep
s to
com
ple
te t
he
squ
are
for
a q
uad
rati
c ex
pre
ssio
n o
f th
e fo
rm a
x2
1bx.
Ste
p 1
Fin
d
.
Ste
p 2
Fin
d 1
22.
Ste
p 3
Add 1
22to
ax
21
bx.
So
lve x
21
6x
13 5
10 b
y c
om
ple
tin
g t
he s
qu
are.
x2
16x
13 5
10
Origin
al equation
x2
16
x1
3 2
3 5
10 2
3S
ubtr
act
3 f
rom
each s
ide.
x2
16x
57
Sim
plif
y.
x2
16x
19 5
7 1
9S
ince 1
225
9,
add 9
to e
ach s
ide.
(x1
3)2
516
Facto
r x
21
6x
19.
x1
3 5
64
Take t
he s
quare
root
of
each s
ide.
x5
23 6
4S
implif
y.
x5
23 1
4or
x5
23 2
4
51
52
7
Th
e so
luti
on s
et i
s {2
7,1}.
So
lve e
ach
eq
ua
tio
n b
y c
om
ple
tin
g t
he s
qu
are.
Ro
un
d t
o t
he n
ea
rest
ten
th i
fn
ecess
ary.
1.
t22
4t
13 5
02.
y2
110y
52
93.
y2
28y
29 5
0
1,3
21,
29
21,9
4.
x2
26x
516
5.
p2
24p
25 5
06.
x2
212x
59
22,8
21,5
20.7
,12.7
7.
c21
8c
520
8.
p2
52p
11
9.
x2
120x
111 5
28
210,2
20.4
,2.4
219,
21
10.x
22
1 5
5x
11.
a2
522a
123
12.
m2
28
m5
27
20.2
,5.2
21,23
1,7
13.x
21
10x
524
14.
a2
218a
519
15.
b2
116b
52
16
212,2
21,19
214.9
,2
1.1
16.4x
25
24 1
4x
17.
2m
21
4m
12 5
818.
4k
25
40k
144
22,3
23,1
21,11
6 } 2
b } 2b } 2b } 2
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y C
om
ple
tin
g t
he S
qu
are
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-3
10-3
Example
Example
Exercises
Exercises
Answers (Lesson 10-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y C
om
ple
tin
g t
he S
qu
are
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-3
10-3
©G
lencoe/M
cG
raw
-Hill
593
Gle
ncoe A
lgebra
1
Lesson 10-3
So
lve e
ach
eq
ua
tio
n b
y t
ak
ing
th
e s
qu
are r
oo
t o
f ea
ch
sid
e.
Ro
un
d t
o t
he n
ea
rest
ten
th i
f n
ecess
ary.
1.
c22
12c
136 5
44,8
2.
w2
210w
125 5
16
1,9
3.
b2
116b
164 5
92
11,
25
4.
y2
12
y1
1 5
32
2.7
,0.7
5.
r21
4r
14 5
72
4.6
,0.6
6.
a2
28a
116 5
12
0.5
,7.5
Fin
d t
he v
alu
e o
f c
tha
t m
ak
es
ea
ch
trin
om
ial
a p
erfe
ct
squ
are.
7.
g2
16
g1
c9
8.
y2
14
y1
c4
9.
a2
214a
1c
49
10.
n2
22
n1
c1
11.s2
218s
1c
81
12.
p2
120p
1c
10
0
So
lve e
ach
eq
ua
tio
n b
y c
om
ple
tin
g t
he s
qu
are.
Ro
un
d t
o t
he n
ea
rest
ten
th i
fn
ecess
ary.
13.x
21
4x
212 5
02,
26
14.
v2
28v
115 5
03,5
15.q
21
6q
57
27,1
16.
r22
2r
515
23,5
17.m
22
14m
130 5
62,12
18.
b2
112b
121 5
10
211,
21
19.z2
24z
11 5
00.3
,3.7
20.
y2
26
y1
4 5
00.8
,5.2
21.r2
28r
110 5
01.6
,6.4
22.
p2
22p
55
21.4
,3.4
23.2a
21
20a
52
22
9.9
,2
0.1
24.
0.5
g2
18g
52
72
15.1
,2
0.9
©G
lencoe/M
cG
raw
-Hill
594
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n b
y t
ak
ing
th
e s
qu
are r
oo
t o
f ea
ch
sid
e.
Ro
un
d t
o t
he n
ea
rest
ten
th i
f n
ecess
ary.
1.
b2
214b
149 5
64
2.
s21
16s
164 5
100
3.
h2
28
h1
16 5
15
21,15
218,2
0.1
,7.9
4.
a2
16a
19 5
27
5.
p2
220p
1100 5
28
6.
u2
110u
125 5
90
28.2
,2.2
4.7
,15.3
214.5
,4.5
Fin
d t
he v
alu
e o
f c
tha
t m
ak
es
ea
ch
trin
om
ial
a p
erfe
ct
squ
are.
7.
t22
24t
1c
14
48.
b2
128b
1c
19
69.
y2
140y
1c
40
0
10.m
21
3m
1c
11.
g2
29
g1
c12.
v2
2v
1c
So
lve e
ach
eq
ua
tio
n b
y c
om
ple
tin
g t
he s
qu
are.
Ro
un
d t
o t
he n
ea
rest
ten
th i
fn
ecess
ary.
13.w
22
14w
124 5
014.
p2
112p
513
15.
s22
30s
156 5
225
2,12
213,1
3,27
16.v
21
8v
19 5
017.
t22
10t
16 5
27
18.
n2
118n
150 5
9
26.6
,2
1.4
1.5
,8.5
215.3
,2
2.7
19.3u
21
15u
23 5
020.
4c2
272 5
24c
21.
0.9
a2
15.4
a2
4 5
0
25.2
,0.2
22.2
,8.2
26
,
22.0.4
h2
10.8
h5
0.2
23.
x2
2x
210 5
024.
x2
1x
22 5
0
22.2
,0.2
24,5
27.1
,1.1
BU
SIN
ES
SF
or E
xercis
es
25 a
nd
26,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Jaim
e ow
ns
a b
usi
nes
s m
ak
ing d
ecor
ati
ve
box
es t
o st
ore
jew
elry
,m
emen
tos,
an
d o
ther
valu
able
s.T
he
fun
ctio
n y
5x
21
50x
11800 m
odel
s th
e p
rofi
t y
that
Jaim
e h
as
mad
e in
mon
th x
for
the
firs
t tw
o yea
rs o
f h
is b
usi
nes
s.
25.W
rite
an
equ
ati
on r
epre
sen
tin
g t
he
mon
th i
n w
hic
h J
aim
e’s
pro
fit
is $
2400.
x2
15
0x
11800 5
24
00
26.U
se c
omp
leti
ng t
he
squ
are
to
fin
d o
ut
in w
hic
h m
onth
Jaim
e’s
pro
fit
is $
2400.
the t
en
th m
on
th
27.P
HY
SIC
SF
rom
a h
eigh
t of
256 f
eet
abov
e a l
ak
e on
a c
liff
,M
ikael
a t
hro
ws
a r
ock
ou
tov
er t
he
lak
e.T
he
hei
gh
t H
of t
he
rock
tse
con
ds
aft
er M
ikael
a t
hro
ws
it i
s re
pre
sen
ted
by t
he
equ
ati
on H
52
16t2
132t
1256.T
o th
e n
eare
st t
enth
of
a s
econ
d,h
ow l
ong d
oes
it t
ak
e th
e ro
ck t
o re
ach
th
e la
ke
bel
ow?
(Hin
t:R
epla
ce H
wit
h 0
.)5.1
s3 } 21 } 4
1 } 21 } 2
2 } 32 } 3
1 } 481
} 49 } 4
Pra
cti
ce (
Avera
ge)
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y C
om
ple
tin
g t
he S
qu
are
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-3
10-3
Answers (Lesson 10-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y C
om
ple
tin
g t
he S
qu
are
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-3
10-3
©G
lencoe/M
cG
raw
-Hill
595
Gle
ncoe A
lgebra
1
Lesson 10-3
Pre
-Act
ivit
yH
ow
did
an
cie
nt
ma
them
ati
cia
ns
use
sq
ua
res
to s
olv
e a
lgeb
ra
iceq
ua
tio
ns?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
0-3
at
the
top
of
page
539 i
n y
our
textb
ook
.
To
solv
e th
e p
roble
m,h
ow m
an
y “
un
its”
wou
ld A
l-K
hw
ari
zmi
have
ad
ded
to
each
sid
e of
th
e eq
uati
on?
16
Read
ing
th
e L
ess
on
1.
Dra
w a
lin
e u
nd
er e
ach
qu
ad
rati
c eq
uati
on t
hat
you
cou
ld s
olve
by t
ak
ing t
he
squ
are
root
of
each
sid
e.
x2
16x
19 5
100
x2
214x
140 5
25
x2
216x
164 5
26
x2
220x
180 5
16
x2
110x
136 5
49
x2
212x
136 5
6
2.
How
can
you
tel
l w
het
her
it
is p
ossi
ble
to
solv
e a q
uad
rati
c eq
uati
on b
y t
ak
ing t
he
squ
are
roo
t of
each
sid
e?
Sam
ple
an
sw
er:
Ch
eck t
o b
e s
ure
th
at
all t
erm
s t
hat
co
nta
in t
he v
ari
ab
leare
on
th
e s
am
e s
ide o
f th
e e
qu
ati
on
.N
ext,
ch
eck w
heth
er
the q
uad
rati
cexp
ressio
n i
s a
perf
ect
sq
uare
.F
inally,
ch
eck t
hat
the n
um
ber
on
th
e s
ide
that
co
nta
ins n
o v
ari
ab
les i
s g
reate
r th
an
or
eq
ual
to 0
.
3.
Exp
lain
how
to
fin
d w
hat
nu
mber
is
nee
ded
for
th
e n
in o
rder
to
mak
e x
22
20x
1n
a p
erfe
ct s
qu
are
.
Fin
d o
ne h
alf
of
220,w
hic
h i
s 2
10,an
d s
qu
are
it.
Th
e r
esu
lt,w
hic
h i
s100,is
th
e r
eq
uir
ed
nu
mb
er.
4.
To
solv
e 3x
22
6x
554 b
y c
omp
leti
ng t
he
squ
are
,w
hy d
oes
it h
elp
fir
st t
o d
ivid
e bot
hsi
des
by 3
?
Sam
ple
an
sw
er:
If y
ou
div
ide b
oth
sid
es b
y 3
,th
e c
oeff
icie
nt
of
x2
will
be
1.It
is t
hen
easy t
o u
se t
he c
oeff
icie
nt
of
xto
decid
e w
hat
nu
mb
er
yo
un
eed
to
ad
d t
o b
oth
sid
es t
o m
ake t
he l
eft
sid
e a
perf
ect
sq
uare
trin
om
ial.
Help
ing
Yo
u R
em
em
ber
5.
Th
e m
eth
od o
f co
mp
leti
ng t
he
squ
are
mig
ht
be
easi
er t
o re
mem
ber
if
you
can
con
nec
t it
to w
hat
you
kn
ow a
bou
t p
erfe
ct s
qu
are
tri
nom
ials
.H
ow i
s co
mp
leti
ng t
he
squ
are
rel
ate
dto
th
e m
eth
od y
ou u
se t
o d
eter
min
e w
het
her
a t
rin
omia
l is
a p
erfe
ct s
qu
are
tri
nom
ial?
Sam
ple
an
sw
er:
If t
he f
irst
an
d l
ast
term
s o
f a t
rin
om
ial
are
perf
ect
sq
uare
s,yo
u m
ult
iply
the p
rod
uct
of
their
sq
uare
ro
ots
by 2
to g
et
the
mid
dle
term
.In
co
mp
leti
ng
th
e s
qu
are
,yo
u c
heck t
hat
the c
oeff
icie
nt
of
x2
is 1
.Th
en
yo
u d
ivid
e t
he c
oeff
icie
nt
of
the x
term
by 2
an
d s
qu
are
th
ere
su
lt t
o g
et
the t
hir
d t
erm
.
©G
lencoe/M
cG
raw
-Hill
596
Gle
ncoe A
lgebra
1
Para
bo
las T
hro
ug
h T
hre
e G
iven
Po
ints
If y
ou k
now
tw
o p
oin
ts o
n a
str
aig
ht
lin
e,you
can
fin
d t
he
equ
ati
on o
fth
e li
ne.
To
fin
d t
he
equ
ati
on o
f a p
ara
bol
a,you
nee
d t
hre
e p
oin
ts o
nth
e cu
rve.
Her
e is
how
to
ap
pro
xim
ate
an
equ
ati
on o
f th
e p
ara
bol
a t
hro
ugh
th
ep
oin
ts (
0,
22),
(3,0),
an
d (
5,2).
Use
th
e gen
eral
equ
ati
on y
5a
x2
1bx
1c.
By s
ubst
itu
tin
g t
he
giv
envalu
es f
or x
an
d y
,you
get
th
ree
equ
ati
ons.
(0,
22):
22 5
c
(3,0):
0 5
9a
13
b1
c
(5,2):
2 5
25a
15b
1c
Fir
st,su
bst
itu
te 2
2 f
or c
in t
he
seco
nd
an
d t
hir
d e
qu
ati
ons.
Th
enso
lve
thos
e tw
o eq
uati
ons
as
you
wou
ld a
ny s
yst
em o
f tw
o eq
uati
ons.
Mu
ltip
ly t
he
seco
nd
equ
ati
on b
y 5
an
d t
he
thir
d e
qu
ati
on b
y 2
3.
0 5
9a
13b
22
Multip
ly b
y 5
.0 5
45a
115b
210
0 5
25a
15
b2
2M
ultip
ly b
y 2
3.
26 5
275a
215b
16
26 5
230a
215b
24
a5
To
fin
d b
,su
bst
itu
te
for
ain
eit
her
th
e se
con
d o
r th
ird
equ
ati
on.
0 5
91
213b
22
b5
Th
e eq
uati
on o
f a p
ara
bol
a t
hro
ugh
th
e th
ree
poi
nts
is
y5
x2
1x
22.
Fin
d t
he e
qu
ati
on
of
a p
ara
bo
la t
hro
ug
h e
ach
set
of
three p
oin
ts.
1.
(1,5),
(0,6),
(2,3)
2.
(25,0),
(0,0),
(8,100)
y5
2x
22
x1
6y
5x
21
x
3.
(4,
24),
(0,1),
(3,
22)
4.
(1,3),
(6,0),
(0,0)
y5
2x
22
x1
6y
52
x2
1x
5.
(2,2),
(5,
23),
(0,
21)
6.
(0,4),
(4,0),
(24,4)
y5
2x
21
x2
1y
52
x2
2x
14
1 } 21 } 8
83
} 30
19
} 30
18
} 53 } 5
1 } 41 } 4
125
} 26
25
} 26
1 } 21 } 2
7} 1
5
1} 1
57} 1
5
1} 1
5
1} 1
5
1} 1
5
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-3
10-3
Answers (Lesson 10-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y U
sin
g t
he Q
uad
rati
c F
orm
ula
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-4
10-4
©G
lencoe/M
cG
raw
-Hill
597
Gle
ncoe A
lgebra
1
Lesson 10-4
Qu
ad
rati
c Fo
rmu
laT
o so
lve
the
stan
dard
for
m o
f th
e qu
ad
rati
c eq
uati
on,
ax
21
bx
1c
50,u
se t
he
Qu
ad
ra
tic F
orm
ula
.
Qu
ad
rati
c F
orm
ula
the f
orm
ula
x5
that
giv
es t
he s
olu
tions o
f ax
21
bx
1c
50,
where
aÞ
02
b6
Ïb
22
w4a
cw
}}
}2
a
So
lve x
21
2x
53 b
yu
sin
g t
he Q
ua
dra
tic F
orm
ula
.
Rew
rite
th
e eq
uati
on i
n s
tan
dard
for
m.
x2
12x
53
Origin
al equation
x2
12
x2
3 5
3 2
3S
ubtr
act
3 f
rom
each s
ide.
x2
12
x2
3 5
0S
implif
y.
Now
let
a5
1,b
52,an
d c
52
3 i
n t
he
Qu
ad
rati
c F
orm
ula
.
x5 5 5
x5
orx
5
51
52
3T
he
solu
tion
set
is
{23,1}.
22 2
4}
22
2 1
4}
2
22 6
Ï16w
}} 2
22 6
Ï(2
)22
w4(1
)(2
w3)w
}}
}2(1
)
2b
6Ï
b2
24
wa
cw}
}}
2a
So
lve x
22
6x
22 5
0 b
yu
sin
g t
he Q
ua
dra
tic F
orm
ula
.R
ou
nd
to
the n
ea
rest
ten
th i
f n
ecess
ary.
For
th
is e
qu
ati
on a
51,b
52
6,an
d c
52
2.
x5 5 5
x5
orx
5
<6.3
<2
0.3
Th
e so
luti
on s
et i
s {2
0.3
,6.3
}.
6 2
Ï44w
}} 2
6 1
Ï44w
}} 2
6 6
Ï44w
}} 2
6 6
Ï(2
6)2
w2
4(1
w)(
22)
w}
}}
2(1
)
2b
6Ï
b2
24
wa
cw}
}}
2a
Example
1Example
1Example
2Example
2
Exercises
Exercises
So
lve e
ach
eq
ua
tio
n b
y u
sin
g t
he Q
ua
dra
tic F
orm
ula
.R
ou
nd
to
th
e n
ea
rest
ten
thif
necess
ary.
1.
x2
23x
12 5
01,2
2.
m2
28
m5
216
43.
16r2
28
r5
21
4.
x2
15x
56
26,1
5.
3x
21
2x
58
22,
6.
8x
22
8x
25 5
02
0.4
,1.4
7.
24
c21
19c
521
,3
8.
2p
21
6p
55
23.7
,0.7
9.
48x
21
22x
215 5
02
,
10.8x
22
4x
524
2,2
11.
2p
21
5p
58
23.6
,1.1
12.
8y
21
9y
24 5
02
1.5
,0.3
13.2x
21
9x
14 5
02
4,
214.
8y
21
17y
12 5
02
2,
2
15.3z2
15
z2
2 5
02
2,
16.
22
x2
18x
14 5
02
0.4
,4.4
17.a
21
3a
52
23.6
,0.6
18.
2y
22
6y
14 5
01,2
1 } 3
1 } 81 } 2
3 } 2
3 } 85 } 6
7 } 4
4 } 3
1 } 4
©G
lencoe/M
cG
raw
-Hill
598
Gle
ncoe A
lgebra
1
Th
e D
iscr
imin
an
tIn
th
e Q
uad
rati
c F
orm
ula
,x
5,th
e ex
pre
ssio
n u
nd
er
the
rad
ical
sign
,b
22
4a
c,is
call
ed t
he
dis
crim
ina
nt.
Th
e d
iscr
imin
an
t ca
n b
e u
sed
to
det
erm
ine
the
nu
mber
of
real
root
s fo
r a q
uad
rati
c eq
uati
on.
Case 1
:C
ase 2
:C
ase 3
:
b2
24
ac
,0
b2
24
ac
50
b2
24
ac
.0
no r
eal ro
ots
one r
eal ro
ot
two r
eal ro
ots
Sta
te t
he v
alu
e o
f th
e d
iscrim
ina
nt
for e
ach
eq
ua
tio
n.T
hen
dete
rm
ine t
he n
um
ber o
f rea
l ro
ots
.
2b
6Ï
b2
24
wa
cw}
}}
2a
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y U
sin
g t
he Q
uad
rati
c F
orm
ula
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-4
10-4
Example
Example
a.
12x
21
5x
54
Wri
te t
he
equ
ati
on i
n s
tan
dard
for
m.
12x
21
5x
54
Origin
al equation
12x
21
5x
24 5
4 2
4S
ubtr
act
4 f
rom
each s
ide.
12x
21
5x
24 5
0S
implif
y.
Now
fin
d t
he
dis
crim
inan
t.
b2
24a
c5
(5)2
24(1
2)(
24)
5217
Sin
ce t
he
dis
crim
inan
t is
pos
itiv
e,th
eeq
uati
on h
as
two
real
root
s.
b.
2x
21
3x
52
4
2x
21
3x
52
4O
rigin
al equation
2x
21
3x
14 5
24 1
4A
dd 4
to e
ach s
ide.
2x
21
3x
14 5
0S
implif
y.
b2
24
ac
5(3
)22
4(2
)(4)
52
23
Sin
ce t
he
dis
crim
inan
t is
neg
ati
ve,
the
equ
ati
on h
as
no
real
root
s.
Exercises
Exercises
Sta
te t
he v
alu
e o
f th
e d
iscrim
ina
nt
for e
ach
eq
ua
tio
n.T
hen
dete
rm
ine t
he n
um
ber
of
rea
l ro
ots
of
the e
qu
ati
on
.
1.
3x
21
2x
23 5
02.
3n
22
7n
28 5
03.
2d
22
10d
29 5
0
40,2 r
eal
roo
ts145,2 r
eal
roo
ts172,2 r
eal
roo
ts
4.
4x
25
x1
45.
3x
22
13x
510
6.
6x
22
10x
110 5
0
65,2 r
eal
roo
ts289,2 r
eal
roo
ts2
140,n
o r
eal
roo
ts
7.
2k
22
20 5
2k
8.
6p
25
211p
240
9.
9 2
18x
19
x2
50
161,2 r
eal
roo
ts2
839,n
o r
eal
roo
ts0,1 r
eal
roo
t
10.12x
21
9 5
26
x11.
9a
25
81
12.
16y
21
16y
14 5
0
2396,n
o r
eal
roo
ts2916,2 r
eal
roo
ts0,1 r
eal
roo
ts
13.8
x2
19
x5
214.
4a
22
4a
14 5
315.
3b
22
18b
52
14
145,2 r
eal
roo
ts0,1 r
eal
roo
t156,2 r
eal
roo
ts
Answers (Lesson 10-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
racti
ce
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y U
sin
g t
he Q
uad
rati
c F
orm
ula
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-4
10-4
©G
lencoe/M
cG
raw
-Hill
599
Gle
ncoe A
lgebra
1
Lesson 10-4
So
lve e
ach
eq
ua
tio
n b
y u
sin
g t
he Q
ua
dra
tic F
orm
ula
.R
ou
nd
to
th
e n
ea
rest
ten
thif
necess
ary.
1.
u2
249 5
02
7,7
2.
n2
2n
220 5
02
4,5
3.
s22
5s
236 5
02
4,9
4.
b2
111b
130 5
02
6,
25
5.
c22
7c
52
30.5
,6.5
6.
p2
14p
52
12
3.7
,2
0.3
7.
a2
29a
122 5
0[
8.
x2
16
x1
3 5
02
5.4
,2
0.6
9.
2x
21
5x
27 5
02
3,1
10.
2h
22
3h
52
1,1
11.2p
21
5p
14 5
0[
12.
2g
21
7g
59
24
,1
13.3t2
12
t2
3 5
02
1.4
,0.7
14.
3x
22
7x
26 5
02
,3
Sta
te t
he v
alu
e o
f th
e d
iscrim
ina
nt
for e
ach
eq
ua
tio
n.T
hen
dete
rm
ine t
he n
um
ber
of
rea
l ro
ots
of
the e
qu
ati
on
.
15.q
21
4q
13 5
016.
m2
12
m1
1 5
0
4;
2 r
eal
roo
ts0;
1 r
eal
roo
t
17.a
22
4a
110 5
018.
w2
26
w1
7 5
0
224;
no
real
roo
ts8;
2 r
eal
roo
ts
19.z2
22z
27 5
020.
y2
210y
125 5
0
32;
2 r
eal
roo
ts0;
1 r
eal
roo
t
21.2d
21
5d
28 5
022.
2s2
16s
112 5
0
89;
2 r
eal
roo
ts2
60;
no
real
roo
ts
23.2u
22
4u
110 5
024.
3h
21
7h
13 5
0
264;
no
real
roo
ts13;
2 r
eal
roo
ts
2 } 3
1 } 2
1 } 21 } 2
©G
lencoe/M
cG
raw
-Hill
600
Gle
ncoe A
lgebra
1
So
lve e
ach
eq
ua
tio
n b
y u
sin
g t
he Q
ua
dra
tic F
orm
ula
.R
ou
nd
to
th
e n
ea
rest
ten
thif
necess
ary.
1.
g2
12
g2
3 5
02
3,1
2.
a2
18a
17 5
02
7,
21
3.
v2
24v
16 5
0[
4.
d2
26
d1
7 5
01.6
,4.4
5.
2z2
19
z2
5 5
02
5,
6.
2r2
112r
110 5
025,
21
7.
2b
22
9b
52
12
[8.
2h
22
5h
512
21
,4
9.
3p
21
p5
42
1,1
10.3m
22
1 5
28
m22.8
,0.1
11.
4y
21
7y
515
23,1
12.
1.6
n2
12
n1
2.5
50
[
13.4.5
k2
14
k2
1.5
50
14.
c21
2c
15
015.
3w
22
w5
21.2
,0.3
23,
21
20.3
,0.6
Sta
te t
he v
alu
e o
f th
e d
iscrim
ina
nt
for e
ach
eq
ua
tio
n.T
hen
dete
rm
ine t
he n
um
ber
of
rea
l ro
ots
of
the e
qu
ati
on
.
16.a
21
8a
116 5
017.
c21
3c
112 5
018.
2w
21
12w
52
7
0;
1 r
eal
roo
t2
39;
no
real
roo
ts88;
2 r
eal
roo
ts
19.2u
21
15u
52
30
20.
4n
21
9 5
12n
21.
3g
22
2g
53.5
215;
no
real
roo
ts0;
1 r
eal
roo
t46;
2 r
eal
roo
ts
22.2.5
k2
13
k2
0.5
50
23.
d2
23
d5
24
24.
s25
2s
21
14;
2 r
eal
roo
ts2
3;
no
real
roo
ts0;
1 r
eal
roo
t
CO
NS
TR
UC
TIO
NF
or E
xercis
es
25 a
nd
26,
use
th
e f
oll
ow
ing
in
form
ati
on
.
A r
oofe
r to
sses
a p
iece
of
roof
ing t
ile
from
a r
oof
onto
th
e gro
un
d 3
0 f
eet
bel
ow.H
e to
sses
th
eti
le w
ith
an
in
itia
l d
own
ward
vel
ocit
y o
f 10 f
eet
per
sec
ond
.
25.W
rite
an
equ
ati
on t
o fi
nd
how
lon
g i
t ta
kes
th
e ti
le t
o h
it t
he
gro
un
d.U
se t
he
mod
el f
orver
tica
l m
otio
n,H
52
16t2
1vt
1h
,w
her
e H
is t
he
hei
gh
t of
an
obje
ct a
fter
tse
con
ds,
vis
th
e in
itia
l vel
ocit
y,an
d h
is t
he
init
ial
hei
gh
t.(H
int:
Sin
ce t
he
obje
ct i
s th
row
n d
own
,th
e in
itia
l vel
ocit
y i
s n
egati
ve.
)H
52
16
t22
10
t1
30
26.H
ow l
ong d
oes
it t
ak
e th
e ti
le t
o h
it t
he
gro
un
d?
ab
ou
t 1.1
s
27.P
HY
SIC
SL
up
e to
sses
a b
all
up
to
Qu
yen
,w
ait
ing a
t a t
hir
d-s
tory
win
dow
,w
ith
an
init
ial
vel
ocit
y o
f 30 f
eet
per
sec
ond
.S
he
rele
ase
s th
e ball
fro
m a
hei
gh
t of
6 f
eet.
Th
eeq
uati
on h
52
16t2
130t
16 r
epre
sen
ts t
he
hei
gh
t h
of t
he
ball
aft
er t
seco
nd
s.If
th
eball
mu
st r
each
a h
eigh
t of
25 f
eet
for
Qu
yen
to
catc
h i
t,d
oes
the
ball
rea
ch Q
uyen
?E
xp
lain
.(H
int:
Su
bst
itu
te 2
5 f
or h
an
d u
se t
he
dis
crim
inan
t.)
No
;th
e d
iscri
min
an
t,2
316,is
neg
ati
ve
,so
th
ere
is n
o s
olu
tio
n.
1 } 43 } 4
1 } 23 } 4
3 } 21 } 2
1 } 4
1 } 31 } 2
1 } 2
Pra
cti
ce (
Avera
ge)
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y U
sin
g t
he Q
uad
rati
c F
orm
ula
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-4
10-4
Answers (Lesson 10-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
So
lvin
g Q
uad
rati
c E
qu
ati
on
s b
y U
sin
g t
he Q
uad
rati
c F
orm
ula
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-4
10-4
©G
lencoe/M
cG
raw
-Hill
601
Gle
ncoe A
lgebra
1
Lesson 10-4
Pre
-Act
ivit
yH
ow
ca
n t
he Q
ua
dra
tic F
orm
ula
be u
sed
to
so
lve p
ro
ble
ms
inv
olv
ing
po
pu
lati
on
tren
ds?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
0-4
at
the
top
of
page
546 i
n y
our
textb
ook
.
You
r te
ach
er a
sks
you
to
pre
dic
t w
hen
17%
of
the
pop
ula
tion
wil
l co
nsi
st o
fp
eop
le b
orn
ou
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e th
e U
nit
ed S
tate
s.W
hat
equ
ati
on s
hou
ld y
ou u
se t
om
ak
e th
e p
red
icti
on?
17 5
0.0
06
t22
0.0
80
t1
5.2
81
Read
ing
th
e L
ess
on
1.
Su
pp
ose
you
wan
t to
sol
ve
12
x2
17x
515 u
sin
g t
he
Qu
ad
rati
c F
orm
ula
.
a.
Wh
at
shou
ld y
ou d
o fi
rst?
Rew
rite
th
e e
qu
ati
on
in
th
e f
orm
ax
21
bx
1c
50.
b.
Wh
at
are
th
e valu
es y
ou n
eed
to
subst
itu
te f
or a
,b
,an
d c
in t
he
Qu
ad
rati
c F
orm
ula
?
a5
12,b
57,an
d c
52
15
c.
Ap
ply
th
e Q
uad
rati
c F
orm
ula
usi
ng t
he
abov
e valu
es,bu
t d
o n
ot s
olve
the
equ
ati
on.
x5
2.a
.Y
ou c
an
use
th
e d
iscr
imin
an
t to
det
erm
ine
the
nu
mber
of
real
root
s fo
r a q
uad
rati
ceq
uati
on.W
hat
is t
he
dis
crim
inan
t?
Th
e d
iscri
min
an
t is
th
e e
xp
ressio
n u
nd
er
the r
ad
ical
sig
n i
n t
he
Qu
ad
rati
c F
orm
ula
,b
22
4a
c.
b.
Com
ple
te t
he
state
men
ts b
elow
so
that
each
sta
tem
ent
is t
rue.
Wh
en t
he
valu
e of
th
e d
iscr
imin
an
t is
,th
ere
is o
ne
real
root
.
Wh
en t
he
valu
e of
th
e d
iscr
imin
an
t is
,th
ere
are
tw
o re
al
root
s.
Wh
en t
he
valu
e of
th
e d
iscr
imin
an
t is
,th
ere
are
no
real
root
s.
Help
ing
Yo
u R
em
em
ber
3.
To
hel
p r
emem
ber
th
e m
eth
ods
for
solv
ing a
qu
ad
rati
c eq
uati
on,ex
pla
in h
ow y
ou w
ould
choo
se t
he
bes
t m
eth
od f
or s
olvin
g a
qu
ad
rati
c eq
uati
on a
x2
1bx
1c
50.
Sam
ple
an
sw
er:
Use g
rap
hin
g f
or
ap
pro
xim
ate
so
luti
on
s.U
se t
he
Qu
ad
rati
c F
orm
ula
fo
r exact
so
luti
on
s.U
se f
acto
rin
g w
hen
th
e f
acto
rsare
easy t
o d
ete
rmin
e.U
se c
om
ple
tin
g t
he s
qu
are
wh
en
bis
an
even
nu
mb
er.
neg
ati
ve
po
sit
ive
ze
ro
27 6
Ï7
22
4w
(12)(
2w
15)
w}
}}
2(1
2)
©G
lencoe/M
cG
raw
-Hill
602
Gle
ncoe A
lgebra
1
Mech
an
ical
Co
nstr
ucti
on
s o
f P
ara
bo
las
A g
iven
lin
e an
d a
poi
nt
det
erm
ine
a p
ara
bol
a.
Her
e is
on
e w
ay t
o co
nst
ruct
th
e cu
rve.
Use
a r
igh
t tr
ian
gle
AB
C(o
r a s
tiff
pie
ce o
f re
ctan
gu
lar
card
boa
rd).
Pla
ce o
ne
leg o
f th
e tr
ian
gle
on
th
e giv
en l
ine
d.
Fast
en o
ne
end
of
a s
trin
g w
ith
len
gth
BC
at
the
giv
en p
oin
t F
an
d t
he
oth
er e
nd
to
the
tria
ngle
at
poi
nt
B.
Pu
t th
e ti
p o
f a p
enci
l at
poi
nt
Pan
d k
eep
th
e st
rin
g t
igh
t.
As
you
mov
e th
e tr
ian
gle
alo
ng t
he
lin
e d
,th
e p
oin
t of
you
r p
enci
l w
ill
trace
a p
ara
bol
a.
Dra
w t
he p
ara
bo
la d
ete
rm
ined
by
lin
e d
an
d p
oin
t F
.
1.
2.
3.
4.
5.
Use
you
r d
raw
ings
to c
omp
lete
th
is c
oncl
usi
on.T
he
gre
ate
r th
e d
ista
nce
of
poi
nt
Ffr
om
lin
e d
,th
e w
ider
the o
pen
ing
of
the p
ara
bo
la.
d
F
d
F
d
F
d
F
FPC
A
B
d
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-4
10-4
Answers (Lesson 10-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Exp
on
en
tial
Fu
ncti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-5
10-5
©G
lencoe/M
cG
raw
-Hill
603
Gle
ncoe A
lgebra
1
Lesson 10-5
Gra
ph
Exp
on
en
tial
Fu
nct
ion
s
Exp
on
en
tial
Fu
ncti
on
a f
unction d
efined b
y a
n e
quation o
f th
e f
orm
y5
ax,
where
a.
0 a
nd a
Þ1
You
can
use
valu
es o
f x
to f
ind
ord
ered
pair
s th
at
sati
sfy a
n e
xp
onen
tial
fun
ctio
n.T
hen
you
can
use
th
e or
der
ed p
air
s to
gra
ph
th
e fu
nct
ion
.
Gra
ph
y5
3x.
Sta
te
the y
-in
tercep
t.
Th
e y-i
nte
rcep
t is
1.
x
y
O
xy
22
}1 9}
21
}1 3}
01
13
29
Gra
ph
y5
12x
.U
se t
he
gra
ph
to
dete
rm
ine t
he a
pp
ro
xim
ate
va
lue o
f 1
220
.5.
Th
e valu
e of
122
0.5
is a
bou
t 2.
1 } 4
x
y
O2
8
xy
22
16
21
4
01
1}1 4}
2} 11 6}
1 } 4
1 } 4
Example
1Example
1Example
2Example
2
Exercises
Exercises
1.
Gra
ph
y5
0.3
x.S
tate
th
e y-i
nte
rcep
t.T
hen
use
th
e gra
ph
to
det
erm
ine
the
ap
pro
xim
ate
valu
e of
0.3
21.5
.U
se a
calc
ula
tor
to
con
firm
th
e valu
e.1;
ab
ou
t 6
Gra
ph
ea
ch
fu
ncti
on
.S
tate
th
e y
-in
tercep
t.
2.
y5
3x
11
23.
y5
12x
11
24.
y5
12x
22
21 x
y
O
x
y
O1
2
x
y
O1
2
1 } 21 } 3
x
y
O1
2
©G
lencoe/M
cG
raw
-Hill
604
Gle
ncoe A
lgebra
1
Iden
tify
Exp
on
en
tial
Beh
avio
rIt
is
som
etim
es u
sefu
l to
kn
ow i
f a s
et o
f d
ata
is
exp
onen
tial.
On
e w
ay t
o te
ll i
s to
obse
rve
the
shap
e of
th
e gra
ph
.A
not
her
way i
s to
obse
rve
the
patt
ern
in
th
e se
t of
data
.
Dete
rm
ine w
heth
er t
he s
et
of
da
ta d
isp
lay
s ex
po
nen
tia
l b
eh
av
ior.
x0
24
68
10
y64
32
16
84
2
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Exp
on
en
tial
Fu
ncti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-5
10-5
Example
Example
Meth
od
1:G
rap
h t
he
Data
Th
e gra
ph
sh
ows
rap
idly
dec
reasi
ng
valu
es o
f y
as
xin
crea
ses.
Th
is i
sch
ara
cter
isti
c of
exp
onen
tial
beh
avio
r.
x
y
O2
8
Meth
od
2:L
ook
for
a P
att
ern
Th
e d
omain
valu
es i
ncr
ease
by r
egu
lar
inte
rvals
of
2,w
hil
e th
e ra
nge
valu
es h
ave
a
com
mon
fact
or o
f .S
ince
th
e d
omain
valu
es i
ncr
ease
by r
egu
lar
inte
rvals
an
d t
he
ran
ge
valu
es h
ave
a c
omm
on f
act
or,th
ed
ata
are
pro
bably
exp
onen
tial.
1 } 2
Exercises
Exercises
Dete
rm
ine w
heth
er t
he d
ata
in
ea
ch
ta
ble
dis
pla
y e
xp
on
en
tia
l b
eh
av
ior.
Ex
pla
inw
hy
or w
hy
no
t.
1.
2.
No
;th
e d
om
ain
valu
es a
re a
t re
gu
lar
Y
es;
the d
om
ain
valu
es a
re a
tin
terv
als
,an
d t
he r
an
ge v
alu
es h
ave
reg
ula
r in
terv
als
,an
d t
he r
an
ge
a c
om
mo
n d
iffe
ren
ce 5
.valu
es h
ave a
co
mm
on
facto
r 3.
3.
4.
Yes;
the d
om
ain
valu
es a
re a
t N
o;
the d
om
ain
valu
es a
re a
tre
gu
lar
inte
rvals
,an
d t
he r
an
ge
reg
ula
r in
terv
als
,b
ut
the r
an
ge
valu
es h
ave a
co
mm
on
facto
r .
valu
es d
o n
ot
ch
an
ge
.
5.
6.
Yes;
the d
om
ain
valu
es a
re a
t Y
es;
the d
om
ain
valu
es a
re a
tre
gu
lar
inte
rvals
,an
d t
he r
an
ge
reg
ula
r in
terv
als
,an
d t
he r
an
ge
valu
es h
ave a
co
mm
on
facto
r 0.5
.valu
es h
ave a
co
mm
on
facto
r .
1 } 3
x0
12
34
y}1 3}
}1 9}} 21 7}
} 81 1}} 2
1 43}
x2
50
510
y1
0.5
0.2
50.1
25
1 } 2
x2
10
12
3
y3
33
33
x2
11
35
y32
16
84
x0
12
3
y3
927
81
x0
12
3
y5
10
15
20
Answers (Lesson 10-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
Exp
on
en
tial
Fu
ncti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-5
10-5
©G
lencoe/M
cG
raw
-Hill
605
Gle
ncoe A
lgebra
1
Lesson 10-5
Gra
ph
ea
ch
fu
ncti
on
.S
tate
th
e y
-in
tercep
t.T
hen
use
th
e g
ra
ph
to
dete
rm
ine t
he
ap
pro
xim
ate
va
lue o
f th
e g
iven
ex
press
ion
.U
se a
ca
lcu
lato
r t
o c
on
firm
th
e v
alu
e.
1.
y5
2x;2
2.3
2.
y5
12x
;1
221.6
1;
4.9
1;
5.8
Gra
ph
ea
ch
fu
ncti
on
.S
tate
th
e y
-in
tercep
t.
3.
y5
3(2
x)
4.
y5
3x
12
33
Dete
rm
ine w
heth
er t
he d
ata
in
ea
ch
ta
ble
dis
pla
y e
xp
on
en
tia
l b
eh
av
ior.
Ex
pla
inw
hy
or w
hy
no
t.
5.
6.
No
;th
e d
om
ain
valu
es a
re a
t Y
es;
the d
om
ain
valu
es a
re a
t re
gu
lar
inte
rvals
an
d t
he r
an
ge
reg
ula
r in
terv
als
an
d t
he r
an
ge
valu
es h
ave a
co
mm
on
valu
es h
ave a
co
mm
on
facto
r 0.5
.d
iffe
ren
ce 3
.
7.
8.
Yes;
the d
om
ain
valu
es a
re a
t N
o;
the d
om
ain
valu
es a
re a
t re
gu
lar
inte
rvals
an
d t
he r
an
ge
reg
ula
r in
terv
als
an
d t
he r
an
ge
valu
es h
ave a
co
mm
on
facto
r 2.
valu
es h
ave a
co
mm
on
d
iffe
ren
ce 2
0.
x50
30
10
210
y90
70
50
30
x4
812
16
y20
40
80
160
x0
510
15
y20
10
52.5
x2
32
22
10
y9
12
15
18
x
y
Ox
y
O
x
y
Ox
y
O
1 } 31 } 3
©G
lencoe/M
cG
raw
-Hill
606
Gle
ncoe A
lgebra
1
Gra
ph
ea
ch
fu
ncti
on
.S
tate
th
e y
-in
tercep
t.T
hen
use
th
e g
ra
ph
to
dete
rm
ine t
he
ap
pro
xim
ate
va
lue o
f th
e g
iven
ex
press
ion
.U
se a
ca
lcu
lato
r t
o c
on
firm
th
e v
alu
e.
1.
y5
12x
;1
220.5
1;
3.2
2.
y5
3x;3
1.9
1;
8.1
3.
y5
12x
;1
221.4
1;
7.0
Gra
ph
ea
ch
fu
ncti
on
.S
tate
th
e y
-in
tercep
t.
4.
y5
4(2
x)
11
55.
y5
2(2
x2
1)
06.
y5
0.5
(3x
23)
21
Dete
rm
ine w
heth
er t
he d
ata
in
ea
ch
ta
ble
dis
pla
y e
xp
on
en
tia
l b
eh
av
ior.
Ex
pla
inw
hy
or w
hy
no
t.
7.
8.
Yes;
the d
om
ain
valu
es a
re a
t N
o;
the d
om
ain
valu
es a
re a
t re
gu
lar
inte
rvals
an
d t
he r
an
ge
reg
ula
r in
terv
als
an
d t
he r
an
ge
valu
es h
ave a
co
mm
on
valu
es h
ave a
co
mm
on
fa
cto
r 0.2
5.
dif
fere
nce 7
.
9.LE
AR
NIN
GM
s.K
lem
per
er t
old
her
En
gli
sh c
lass
th
at
each
wee
k s
tud
ents
ten
d t
o fo
rget
one
sixth
of
the
voc
abu
lary
wor
ds
they
lea
rned
th
e p
revio
us
wee
k.S
up
pos
e a s
tud
ent
learn
s 60 w
ord
s.T
he
nu
mber
of
wor
ds
rem
ember
ed c
an
be
des
crib
ed b
y t
he
fun
ctio
n
W(x
) 5
601
2x,w
her
e x
is t
he
nu
mber
of
wee
ks
that
pass
.H
ow m
an
y w
ord
s w
ill
the
stu
den
t re
mem
ber
aft
er 3
wee
ks?
ab
ou
t 35
10.B
IOLO
GY
Su
pp
ose
a c
erta
in c
ell
rep
rod
uce
s it
self
in
fou
r h
ours
.If
a l
ab r
esea
rch
erbeg
ins
wit
h 5
0 c
ells
,h
ow m
an
y c
ells
wil
l th
ere
be
aft
er o
ne
day,
two
days,
an
d t
hre
ed
ays?
(H
int:
Use
th
e ex
pon
enti
al
fun
ctio
n y
550(2
x).
)3200 c
ells;
204,8
00 c
ells;
13,1
07,2
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5 } 6
x21
18
15
12
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16
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x
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y
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y
O
1 } 41 } 4
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01
} 10
Pra
cti
ce (
Avera
ge)
Exp
on
en
tial
Fu
ncti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-5
10-5
Answers (Lesson 10-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
Exp
on
en
tial
Fu
ncti
on
s
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-5
10-5
©G
lencoe/M
cG
raw
-Hill
607
Gle
ncoe A
lgebra
1
Lesson 10-5
Pre
-Act
ivit
yH
ow
ca
n e
xp
on
en
tia
l fu
ncti
on
s b
e u
sed
in
art?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
0-5
at
the
top
of
page
554 i
n y
our
textb
ook
.
If M
r.W
art
her
had
carv
ed a
nin
th l
ayer
of
pli
ers,
how
man
y p
lier
s w
ould
he
have
carv
ed?
29
or
512 p
liers
Read
ing
th
e L
ess
on
1.
Th
e gra
ph
s of
tw
o ex
pon
enti
al
fun
ctio
ns
of t
he
form
y5
ax
are
sh
own
bel
ow.
A.
B.
a.
In G
rap
h A
,th
e valu
e of
ais
gre
ate
r th
an
an
d l
ess
than
.T
he
yvalu
es d
ecre
ase
as
the
xvalu
es
.
b.
In G
rap
h B
,th
e valu
e of
ais
gre
ate
r th
an
.T
he
yvalu
es
as
the
xvalu
es i
ncr
ease
.
2.a
.W
hen
you
loo
k f
or a
patt
ern
of
exp
onen
tial
beh
avio
r in
a s
et o
f d
ata
,w
hat
is t
he
patt
ern
you
are
loo
kin
g f
or?
Valu
es o
f x
(do
main
valu
es)
that
are
at
reg
ula
r in
terv
als
an
d v
alu
es o
fy
(ran
ge v
alu
es)
that
have a
co
mm
on
facto
r.
b.
If a
set
of
data
has
a n
egati
ve
com
mon
fact
or,d
oes
it d
isp
lay e
xp
onen
tial
beh
avio
r?
No
;th
e c
om
mo
n f
acto
r n
eed
s t
o b
e g
reate
r th
an
0 a
nd
no
t eq
ual
to 1
.
Help
ing
Yo
u R
em
em
ber
3.
Wh
at
com
pari
son
s ca
n y
ou m
ak
e bet
wee
n t
he
qu
ad
rati
c fu
nct
ion
y5
x2
an
d t
he
exp
onen
tial
fun
ctio
n y
52
xto
hel
p r
emem
ber
th
e d
iffe
ren
ces
bet
wee
n q
uad
rati
c an
dex
pon
enti
al
fun
ctio
ns?
Sam
ple
an
sw
er:
In t
he q
uad
rati
c f
un
cti
on
,th
e v
ari
ab
le i
s t
he b
ase a
nd
the e
xp
on
en
t is
a n
um
ber;
in t
he e
xp
on
en
tial
fun
cti
on
,th
e v
ari
ab
le i
s t
he
exp
on
en
t an
d t
he b
ase i
s a
nu
mb
er.
incre
ase
1
incre
ase
10
x
y
O
x
y
O
©G
lencoe/M
cG
raw
-Hill
608
Gle
ncoe A
lgebra
1
Wri
tin
g E
xp
ressio
ns o
f A
rea i
n F
acto
red
Fo
rm
Writ
e a
n e
xp
ress
ion
in
fa
cto
red
fo
rm
fo
r t
he a
rea
Ao
f th
e
sha
ded
reg
ion
in
ea
ch
fig
ure b
elo
w.
1.
2.
A5
2r
2(4
2p
)
A5
(x1
y)(
x2
y)
3.
4.
A5
(a1
b)(
a2
b)
A5
r2(8
1p
)
5.
6.
A5
p(R
12
r)(R
22
r)A
5a
(3a
12
b)
7.
8.
A5
x218
22
A5
r2(p
21)
p } 2
r
r
2x
4x
4x
90
8
b
2a
a
a
rr
r
R
rp } 8
4r
rr
b a
r
r
x x
xx
y y
yy
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-5
10-5
Answers (Lesson 10-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swers
Stu
dy G
uid
e a
nd I
nte
rven
tion
Gro
wth
an
d D
ecay
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-6
10-6
©G
lencoe/M
cG
raw
-Hill
609
Gle
ncoe A
lgebra
1
Lesson 10-6
Exp
on
en
tial
Gro
wth
Pop
ula
tion
in
crea
ses
an
d g
row
th o
f m
onet
ary
in
ves
tmen
ts a
reex
am
ple
s of
ex
po
nen
tia
l g
ro
wth
.T
his
mea
ns
that
an
in
itia
l am
oun
t in
crea
ses
at
a s
tead
yra
te o
ver
tim
e.
The g
enera
l equation f
or
exponential gro
wth
is y
5C
(1 1
r)t .
•y
repre
sents
the f
inal am
ount.
Exp
on
en
tial
Gro
wth
•C
repre
sents
the initia
l am
ount.
•r
repre
sents
the r
ate
of
change e
xpre
ssed a
s a
decim
al.
•t
repre
sents
tim
e.
PO
PU
LATIO
NT
he
po
pu
lati
on
of
Jo
hn
son
Cit
y i
n 1
995 w
as
25,0
00.S
ince t
hen
,th
e p
op
ula
tio
n h
as
gro
wn
at
an
av
era
ge r
ate
of
3.2
% e
ach
yea
r.
a.
Writ
e a
n e
qu
ati
on
to
rep
rese
nt
the
po
pu
lati
on
of
Jo
hn
son
Cit
y s
ince 1
995.
Th
e ra
te 3
.2%
can
be
wri
tten
as
0.0
32.
y5
C(1
1r)
t
y5
25,0
00(1
10.0
32)t
y5
25,0
00(1
.032)t
b.
Acco
rd
ing
to
th
e e
qu
ati
on
,w
ha
t w
ill
the p
op
ula
tio
n o
f J
oh
nso
n C
ity
be i
nth
e y
ea
r 2
005?
In 2
005,t
wil
l eq
ual
2005 2
1995 o
r 10.
Su
bst
itu
te 1
0 f
or t
in t
he
equ
ati
on f
rom
p
art
a.
y5
25,0
00(1
.032)1
0t
51
0
<34,2
56
In 2
005,th
e p
opu
lati
on o
f Joh
nso
n C
ity w
ill
be
abou
t 34,2
56.
INV
ES
TM
EN
TT
he
Ga
rcia
s h
av
e $
12,0
00 i
n a
sa
vin
gs
acco
un
t.T
he b
an
k p
ay
s 3.5
% i
nte
rest
on
sa
vin
gs
acco
un
ts,
co
mp
ou
nd
ed
mo
nth
ly.
Fin
d t
he b
ala
nce i
n 3
yea
rs.
Th
e ra
te 3
.5%
can
be
wri
tten
as
0.0
35.
Th
e sp
ecia
l eq
uati
on f
or c
omp
oun
d
inte
rest
is
A5
P11
12n
t ,w
her
e A
rep
rese
nts
th
e bala
nce
,P
is t
he
init
ial
am
oun
t,r
rep
rese
nts
th
e an
nu
al
rate
exp
ress
ed a
s a d
ecim
al,
nre
pre
sen
ts t
he
nu
mber
of
tim
es t
he
inte
rest
is
com
pou
nd
edea
ch y
ear,
an
d t
rep
rese
nts
th
e n
um
ber
of
yea
rs t
he
mon
ey i
s in
ves
ted
.
A5
P11
12n
t
A5
12,0
0011
123
6
A<
12,0
00(1
.00292)3
6
A<
13,3
28.0
9
In t
hre
e yea
rs,th
e bala
nce
of
the
acc
oun
tw
ill
be
$13,3
28.0
9.
0.0
35
}1
2
r } n
r } n
Example
1Example
1Example
2Example
2
Exercises
Exercises
1.P
OP
ULA
TIO
NT
he
pop
ula
tion
of
the
Un
ited
2.IN
VE
ST
ME
NT
Det
erm
ine
the
Sta
tes
has
bee
n i
ncr
easi
ng a
t an
aver
age
am
oun
t of
an
in
ves
tmen
t of
$2500 i
f it
an
nu
al
rate
of
0.9
1%
.If
th
e p
opu
lati
on o
f th
eis
in
ves
ted
at
in i
nte
rest
rate
of
5.2
5%
U
nit
ed S
tate
s w
as
abou
t 284,9
05,4
00 i
n t
he
co
mp
oun
ded
mon
thly
for
4 y
ears
.yea
r 2001,p
red
ict
the
U.S
.p
opu
lati
on i
n t
he
$3082.7
8yea
r 2005.
Sourc
e:
U. S
. Cen
sus
Bure
auab
ou
t 295,4
18,3
75
3.P
OP
ULA
TIO
NIt
is
esti
mate
d t
hat
the
4.IN
VE
ST
ME
NT
Det
erm
ine
the
pop
ula
tion
of
the
wor
ld i
s in
crea
sin
g a
t an
am
oun
t of
an
in
ves
tmen
t of
$100,0
00
aver
age
an
nu
al
rate
of
1.3
%.If
th
e p
opu
lati
on
if i
t is
in
ves
ted
at
an
in
tere
st r
ate
of
of
th
e w
orld
was
abou
t 6,1
67,0
07,0
00 i
n t
he
5.2
% c
omp
oun
ded
qu
art
erly
for
yea
r 2001,p
red
ict
the
wor
ld p
opu
lati
on i
n t
he
12 y
ears
.$185,8
88.8
7yea
r 2010.
Sourc
e:
U. S
. Cen
sus
Bure
auab
ou
t 6,9
27,2
27,4
83
©G
lencoe/M
cG
raw
-Hill
610
Gle
ncoe A
lgebra
1
Exp
on
en
tial
Deca
yR
ad
ioact
ive
dec
ay a
nd
dep
reci
ati
on a
re e
xam
ple
s of
ex
po
nen
tia
ld
eca
y.T
his
mea
ns
that
an
in
itia
l am
oun
t d
ecre
ase
s at
a s
tead
y r
ate
over
a p
erio
d o
f ti
me.
The g
enera
l equation f
or
exponential decay is y
5C
(1 2
r)t.
•y
repre
sents
the f
inal am
ount.
Exp
on
en
tial
Decay
•C
repre
sents
the initia
l am
ount.
•r
repre
sents
the r
ate
of
decay e
xpre
ssed a
s a
decim
al.
•t
repre
sents
tim
e.
DE
PR
EC
IAT
ION
Th
e o
rig
ina
l p
ric
e o
f a
tra
cto
r w
as
$45,0
00.T
he
va
lue o
f th
e t
ra
cto
r d
ecrea
ses
at
a s
tea
dy
ra
te o
f 12%
per y
ea
r.
a.
Writ
e a
n e
qu
ati
on
to
rep
rese
nt
the v
alu
e o
f th
e t
ra
cto
r s
ince i
t w
as
pu
rch
ase
d.
Th
e ra
te 1
2%
can
be
wri
tten
as
0.1
2.
y5
C(1
2r)
tG
enera
l equation f
or
exponential decay
y5
45,0
00(1
20.1
2)t
C5
45,0
00 a
nd r
50.1
2
y5
45,0
00(0
.88)t
Sim
plif
y.
b.
Wh
at
is t
he v
alu
e o
f th
e t
ra
cto
r i
n 5
yea
rs?
y5
45,0
00(0
.88)t
Equation f
or
decay f
rom
part
a
y5
45,0
00(0
.88)5
t5
5
y<
23,7
47.9
4U
se a
calc
ula
tor.
In 5
yea
rs,th
e tr
act
or w
ill
be
wor
th a
bou
t $23,7
47.9
4.
1.P
OP
ULA
TIO
NT
he
pop
ula
tion
of
Bu
lgari
a h
as
bee
n d
ecre
asi
ng a
t an
an
nu
al
rate
of
1.3
%.If
th
e p
opu
lati
on o
f B
ulg
ari
a w
as
abou
t 7,7
97,0
00 i
n t
he
yea
r 2000,
pre
dic
t it
s p
opu
lati
on i
n t
he
yea
r 2010.
Sourc
e:
U. S
. Cen
sus
Bure
auab
ou
t 6,8
41,0
00
2.D
EP
RE
CIA
TIO
NC
arl
Gos
sell
is
a m
ach
inis
t.H
e bou
gh
t so
me
new
mach
iner
yfo
r abou
t $125,0
00.H
e w
an
ts t
o ca
lcu
late
th
e valu
e of
th
e m
ach
iner
y o
ver
th
en
ext
10 y
ears
for
tax p
urp
oses
.If
th
e m
ach
iner
y d
epre
ciate
s at
the
rate
of
15%
per
yea
r,w
hat
is t
he
valu
e of
th
e m
ach
iner
y (
to t
he
nea
rest
$100)
at
the
end
of
10 y
ears
?ab
ou
t $24,6
00
3.A
RC
HA
EO
LO
GY
Th
e h
alf
-lif
eof
a r
ad
ioact
ive
elem
ent
is d
efin
ed a
s th
e ti
me
that
it t
ak
es f
or o
ne-
half
a q
uan
tity
of
the
elem
ent
to d
ecay.
Rad
ioact
ive
Carb
on-1
4 i
s fo
un
d i
n a
ll l
ivin
g o
rgan
ism
s an
d h
as
a h
alf
-lif
e of
5730 y
ears
.C
onsi
der
a l
ivin
g o
rgan
ism
wit
h a
n o
rigin
al
con
cen
trati
on o
f C
arb
on-1
4 o
f 100 g
ram
s.
a.
If t
he
organ
ism
liv
ed 5
730 y
ears
ago,
wh
at
is t
he
con
cen
trati
on o
f C
arb
on-1
4 t
oday?
50 g
b.
If t
he
organ
ism
liv
ed 1
1,4
60 y
ears
ago,
det
erm
ine
the
con
cen
trati
on o
f C
arb
on-1
4 t
oday.
25 g
4.D
EP
RE
CIA
TIO
NA
new
car
cost
s $32,0
00.It
is
exp
ecte
d t
o d
epre
ciate
12%
each
yea
r fo
r 4 y
ears
an
d t
hen
dep
reci
ate
8%
each
yea
r th
erea
fter
.F
ind
th
e valu
e of
the
car
in 6
yea
rs.
ab
ou
t $16,2
42.6
3
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Gro
wth
an
d D
ecay
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-6
10-6
Example
Example
Exercises
Exercises
Answers (Lesson 10-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
racti
ce
Gro
wth
an
d D
ecay
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-6
10-6
©G
lencoe/M
cG
raw
-Hill
611
Gle
ncoe A
lgebra
1
Lesson 10-6
PO
PU
LA
TIO
NF
or E
xercis
es
1 a
nd
2,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Th
e p
opu
lati
on o
f N
ew Y
ork
Cit
y i
ncr
ease
d f
rom
7,3
22,5
64 i
n 1
990 t
o 8,0
08,2
78 i
n 2
000.T
he
an
nu
al
rate
of
pop
ula
tion
in
crea
se f
or t
he
per
iod
was
abou
t 0.9
%.
Sourc
e:
ww
w.n
yc.g
ov
1.
Wri
te a
n e
qu
ati
on f
or t
he
pop
ula
tion
tyea
rs a
fter
1990.
P5
7,3
22,5
64
(1.0
09)t
2.
Use
th
e eq
uati
on t
o p
red
ict
the
pop
ula
tion
of
New
Yor
k C
ity i
n 2
010.
ab
ou
t 8,7
60,0
00
SA
VIN
GS
Fo
r E
xercis
es
3 a
nd
4,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Th
e F
resh
an
d G
reen
Com
pan
y h
as
a s
avin
gs
pla
n f
or i
ts e
mp
loyee
s.If
an
em
plo
yee
mak
esan
in
itia
l co
ntr
ibu
tion
of
$1000,th
e co
mp
an
y p
ays
8%
in
tere
st c
omp
oun
ded
qu
art
erly
.
3.
If a
n e
mp
loyee
part
icip
ati
ng i
n t
he
pla
n w
ith
dra
ws
the
bala
nce
of
the
acc
oun
t aft
er
5 y
ears
,h
ow m
uch
wil
l be
in t
he
acc
oun
t?$1485.9
5
4.
If a
n e
mp
loyee
part
icip
ati
ng i
n t
he
pla
n w
ith
dra
ws
the
bala
nce
of
the
acc
oun
t aft
er
35 y
ears
,h
ow m
uch
wil
l be
in t
he
acc
oun
t?$15,9
96.4
7
5.H
OU
SIN
GM
r.an
d M
rs.B
oyce
bou
gh
t a h
ouse
for
$96,0
00 i
n 1
995.T
he
real
esta
tebro
ker
in
dic
ate
d t
hat
hou
ses
in t
hei
r are
a a
re a
pp
reci
ati
ng a
t an
aver
age
an
nu
al
rate
of
4%
.If
th
e ap
pre
ciati
on r
emain
s st
ead
y a
t th
is r
ate
,w
hat
wil
l be
the
valu
e of
th
e B
oyce
’sh
ome
in 2
005?
ab
ou
t $142,1
03
MA
NU
FAC
TU
RIN
GF
or E
xercis
es
6 a
nd
7,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Zel
ler
Ind
ust
ries
bou
gh
t a p
iece
of
wea
vin
g e
qu
ipm
ent
for
$60,0
00.It
is
exp
ecte
d t
od
epre
ciate
at
an
aver
age
rate
of
10%
per
yea
r.
6.
Wri
te a
n e
qu
ati
on f
or t
he
valu
e of
th
e p
iece
of
equ
ipm
ent
aft
er t
yea
rs.
E5
60,0
00(0
.90)t
7.
Fin
d t
he
valu
e of
th
e p
iece
of
equ
ipm
ent
aft
er 6
yea
rs.
ab
ou
t $31,8
86
8.FIN
AN
CE
SK
yle
saved
$500 f
rom
a s
um
mer
job
.H
e p
lan
s to
sp
end
10%
of
his
savin
gs
each
wee
k o
n v
ari
ous
form
s of
en
tert
ain
men
t.A
t th
is r
ate
,h
ow m
uch
wil
l K
yle
have
left
aft
er 1
5 w
eek
s?$102.9
5
9.T
RA
NS
PO
RTA
TIO
NT
iffa
ny’s
mot
her
bou
gh
t a c
ar
for
$9000 f
ive
yea
rs a
go.
Sh
e w
an
tsto
sel
l it
to
Tif
fan
y b
ase
d o
n a
15%
an
nu
al
rate
of
dep
reci
ati
on.A
t th
is r
ate
,h
ow m
uch
wil
l T
iffa
ny p
ay f
or t
he
car?
ab
ou
t $3993
©G
lencoe/M
cG
raw
-Hill
612
Gle
ncoe A
lgebra
1
CO
MM
UN
ICA
TIO
NS
Fo
r E
xercis
es
1 a
nd
2,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Com
mer
cial
non
-mu
sic
rad
io s
tati
ons
incr
ease
d a
t an
aver
age
an
nu
al
rate
of
3.1
% f
rom
1996 t
o 2000.C
omm
erci
al
rad
io s
tati
ons
in t
his
for
mat
nu
mber
ed 1
262 i
n 1
996.
Sourc
e:
M S
treet
Cor
pora
tion,
Nas
hvill
e, T
N
1.
Wri
te a
n e
qu
ati
on f
or t
he
nu
mber
of
rad
io s
tati
ons
for
tyea
rs a
fter
1996.
R5
1262(1
.031)t
2.
If t
he
tren
d c
onti
nu
es,p
red
ict
the
nu
mber
of
rad
io s
tati
ons
in t
his
for
mat
for
the
yea
r 2006.
ab
ou
t 1713 s
tati
on
s
3.IN
VE
ST
ME
NT
SD
eter
min
e th
e am
oun
t of
an
in
ves
tmen
t if
$500 i
s in
ves
ted
at
an
inte
rest
rate
of
4.2
5%
com
pou
nd
ed q
uart
erly
for
12 y
ears
.$830.4
1
4.IN
VE
ST
ME
NT
SD
eter
min
e th
e am
oun
t of
an
in
ves
tmen
t if
$300 i
s in
ves
ted
at
an
inte
rest
rate
of
6.7
5%
com
pou
nd
ed s
emia
nn
uall
y f
or 2
0 y
ears
.$1131.7
3
5.H
OU
SIN
GT
he
Gre
ens
bou
gh
t a c
ond
omin
ium
for
$110,0
00 i
n 2
000.If
its
valu
eap
pre
ciate
s at
an
aver
age
rate
of
6%
per
yea
r,w
hat
wil
l th
e valu
e be
in 2
005?
ab
ou
t$147,2
05
DE
FO
RE
STA
TIO
NF
or E
xercis
es
6 a
nd
7,
use
th
e f
oll
ow
ing
in
form
ati
on
.
Du
rin
g t
he
1990s,
the
fore
sted
are
a o
f G
uate
mala
dec
rease
d a
t an
aver
age
rate
of
1.7
%.
Sourc
e:
ww
w.w
orld
bank
.org
6.
If t
he
fore
sted
are
a i
n G
uate
mala
in
1990 w
as
abou
t 34,4
00 s
qu
are
kil
omet
ers,
wri
te a
neq
uati
on f
or t
he
fore
sted
are
a f
or t
yea
rs a
fter
1990.
C5
34,4
00(0
.983)t
7.
If t
his
tre
nd
con
tin
ues
,p
red
ict
the
fore
sted
are
a i
n 2
015.
ab
ou
t 22,4
00 k
m2
8.B
US
INE
SS
A p
iece
of
mach
iner
y v
alu
ed a
t $25,0
00 d
epre
ciate
s at
a s
tead
y r
ate
of
10%
yea
rly.
Wh
at
wil
l th
e valu
e of
th
e p
iece
of
mach
iner
y b
e aft
er 7
yea
rs?
ab
ou
t $11,9
57
9.T
RA
NS
PO
RTA
TIO
NA
new
car
cost
s $18,0
00.It
is
exp
ecte
d t
o d
epre
ciate
at
an
aver
age
rate
of
12%
per
yea
r.F
ind
th
e valu
e of
th
e ca
r in
8 y
ears
.ab
ou
t $6473
10.P
OP
ULA
TIO
NT
he
pop
ula
tion
of
Osa
ka,Jap
an
dec
lin
ed a
t an
aver
age
an
nu
al
rate
of
0.0
5%
for
th
e fi
ve
yea
rs b
etw
een
1995 a
nd
2000.If
th
e p
opu
lati
on o
f O
sak
a w
as
11,0
13,0
00 i
n 2
000 a
nd
it
con
tin
ues
to
dec
lin
e at
the
sam
e ra
te,p
red
ict
the
pop
ula
tion
in
2050.
ab
ou
t 10,7
41,0
00
Pra
cti
ce (
Avera
ge)
Gro
wth
an
d D
ecay
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-6
10-6
Answers (Lesson 10-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swers
Readin
g t
o L
earn
Math
em
ati
cs
Gro
wth
an
d D
ecay
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-6
10-6
©G
lencoe/M
cG
raw
-Hill
613
Gle
ncoe A
lgebra
1
Lesson 10-6
Pre
-Act
ivit
yH
ow
ca
n e
xp
on
en
tia
l g
ro
wth
be u
sed
to
pred
ict
futu
re s
ale
s?
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
0-6
at
the
top
of
page
561 i
n y
our
textb
ook
.
Su
pp
ose
you
wan
t to
pre
dic
t th
e am
oun
t of
mon
ey a
n a
ver
age
hou
seh
old
wil
l sp
end
on
res
tau
ran
t m
eals
in
th
e yea
r 2005.W
hat
nu
mber
sh
ould
be
subst
itu
ted
for
t?
11
Read
ing
th
e L
ess
on
Ma
tch
an
eq
ua
tio
n t
o e
ach
sit
ua
tio
n,
an
d t
hen
in
dic
ate
wh
eth
er t
he s
itu
ati
on
is
an
ex
am
ple
of
ex
po
nen
tia
l g
ro
wth
or d
eca
y.
1.
A c
oin
had
a v
alu
e of
$1.1
7 i
n 1
995.It
s valu
e h
as
bee
n i
ncr
easi
ng a
t a r
ate
of
9%
p
er y
ear.
A;
gro
wth
A.
y5
1.1
7(1
.09)t
B.
y5
1.1
7(0
.91)t
2.
A b
usi
nes
s ow
ner
has
just
paid
$6000 f
or a
com
pu
ter.
It d
epre
ciate
s at
a r
ate
of
22%
p
er y
ear.
How
mu
ch w
ill
it b
e w
orth
in
5 y
ears
?B
;d
ecay
A.
A5
6000(1
.22)5
B.
A5
6000(0
.78)5
3.
A c
ity h
ad
a p
opu
lati
on o
f 14,3
58 r
esid
ents
in
1999.S
ince
th
en,it
s p
opu
lati
on h
as
bee
nd
ecre
asi
ng a
t a r
ate
of
abou
t 5.5
% p
er y
ear.
B;
decay
A.
A5
14,3
58(1
.055)t
B.
A5
14,3
58(0
.945)t
4.
Gin
a d
epos
ited
$1500 i
n a
n a
ccou
nt
that
pays
4%
in
tere
st c
omp
oun
ded
qu
art
erly
.W
hat
wil
l be
the
wor
th o
f th
e acc
oun
t in
2 y
ears
if
she
mak
es n
o d
epos
its
an
d n
ow
ith
dra
wals
?B
;g
row
th
A.
A5
1500(1
.02)2
B.
A5
1500(1
.02)8
Help
ing
Yo
u R
em
em
ber
5.
How
can
you
use
wh
at
you
kn
ow a
bou
t ra
isin
g a
nu
mber
to
the
0 p
ower
to
hel
p y
oure
mem
ber
wh
at
Cre
pre
sen
ts i
n t
he
exp
onen
tial
gro
wth
equ
ati
on A
5C
(1 1
r)t
an
d t
he
exp
onen
tial
dec
ay e
qu
ati
on A
5C
(1 2
r)t ?
Sam
ple
an
sw
er:
Th
e i
nit
ial
am
ou
nt
is t
he a
mo
un
t b
efo
re a
ny t
ime h
as
passed
,th
at
is,w
hen
t5
0.W
hen
t5
0,C
(1 1
r)t
5C
(1 1
r)0
5C
(1)
5C
an
d C
(1 2
r)t
5C
(1 2
r)0
5C
(1)
5C
.S
o C
rep
resen
ts t
he i
nit
ial
am
ou
nt.
©G
lencoe/M
cG
raw
-Hill
614
Gle
ncoe A
lgebra
1
Cu
rio
us C
ircle
sT
wo
circ
les
can
be
arr
an
ged
in
fou
r w
ays:
one
circ
le c
an
be
insi
de
the
oth
er,th
ey c
an
be
sep
ara
te,th
ey c
an
over
lap
,or
th
ey c
an
coi
nci
de.
In h
ow m
an
y w
ays
can
a g
iven
nu
mber
of
circ
les
be
eith
er s
epara
te o
rin
sid
e ea
ch o
ther
? (T
he
situ
ati
ons
in w
hic
h t
he
circ
les
over
lap
or
coin
cid
e are
not
cou
nte
d h
ere.
)
For
3 c
ircl
es,th
ere
are
4 d
iffe
ren
t p
ossi
bil
itie
s.
So
lve e
ach
pro
ble
m.
Ma
ke d
ra
win
gs
to s
ho
w y
ou
r a
nsw
ers.
1.
Sh
ow t
he
dif
fere
nt
ways
in w
hic
h 2
cir
cles
can
be
sep
ara
te o
rin
sid
e ea
ch o
ther
.H
ow m
an
y w
ays
are
th
ere?
two
ways
2.
Sh
ow t
he
dif
fere
nt
ways
for
4 c
ircl
es.H
ow m
an
y w
ays
are
th
ere?
nin
e w
ays
3.
Use
you
r an
swer
for
Exer
cise
2 t
o sh
ow t
hat
the
nu
mber
of
ways
for
5 c
ircl
es i
s at
least
18.
Fir
st,
dra
w a
n e
xtr
a c
ircle
next
toeach
of
the w
ays f
or
4 c
ircle
s.T
hen
dra
w a
cir
cle
aro
un
d e
ach
of
the w
ays f
or
4 c
ircle
s.
4.
Fin
d t
he
nu
mber
of
ways
for
5 c
ircl
es.S
how
you
r d
raw
ings
on a
sep
ara
te s
hee
t of
pap
er.
20 w
ays
1 5 8
23
4
67
9
21
23
41
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-6
10-6
Answers (Lesson 10-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Geo
metr
ic S
eq
uen
ces
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-7
10-7
©G
lencoe/M
cG
raw
-Hill
615
Gle
ncoe A
lgebra
1
Lesson 10-7
Geo
metr
ic S
eq
uen
ces
A g
eo
metr
ic s
eq
uen
ce
is a
sequ
en
ce i
n w
hic
h e
ach
term
aft
er
the n
on
zero
fir
st t
erm
is
fou
nd
by m
ult
iply
ing t
he p
revio
us
term
by a
con
stan
t ca
lled
th
eco
mm
on
ra
tio
.
Geo
metr
ic
a s
equence o
f num
bers
of
the f
orm
a,
ar,
ar
2,
ar
3,
…,
Exam
ple
:1,
2,
4,
8,
16,
…
Seq
uen
ce
where
aÞ
0,
and r
Þ0 o
r 1
Dete
rm
ine w
heth
er e
ach
seq
uen
ce i
s g
eo
metr
ic.
Exercises
Exercises
Dete
rm
ine w
heth
er e
ach
seq
uen
ce i
s g
eo
metr
ic.
1.
2,4,6,8,10,…
2.
2,4,8,16,32,…
3.
210,
25,
22.5
,2
1.2
5,…
no
yes
yes
4.
100,400,1600,6400,…
5.
,,
,,…
6.
,,
,,…
yes
no
yes
Fin
d t
he n
ex
t th
ree t
erm
s i
n e
ach
geo
metr
ic s
eq
uen
ce.
7.
100,300,900,2700,…
8.
,,
,,…
9.
80,40,20,10,…
8100,24,3
00,72,9
00
,,
5,
,
Fin
d t
he n
th t
erm
of
ea
ch
geo
metr
ic s
eq
uen
ce.
10.a
15
5,n
56,r
53
11.
a1
53,n
55,r
54
12.
a1
52
5,n
57,r
52
2
1215
768
2320
5 } 4
5 } 2
1} 1
28
1} 6
4
1} 3
2
1} 1
6
1 } 8
1 } 4
1 } 2
1} 8
1
1} 2
7
1 } 9
1 } 3
1 } 5
1 } 4
1 } 3
1 } 2
Example
1Example
1
Example
2Example
2
a.
3,
6,
9,
12,
15,
…
In t
his
sequ
en
ce,each
term
is
fou
nd
by
ad
din
g 3
to t
he p
revio
us
term
.T
he
sequ
en
ce i
s ari
thm
eti
c an
d n
ot
geom
etr
ic.
b.
1,
4,
16,
64,
…
In t
his
sequ
en
ce,each
term
is
fou
nd
by
mu
ltip
lyin
g t
he p
revio
us
term
by 4
.T
he
sequ
en
ce i
s geom
etr
ic.
a.
8,
24,
2,
21,
…
Th
e c
om
mon
fact
or
is
or
2.U
se t
his
info
rmati
on
to f
ind
th
e n
ext
thre
e t
erm
s.
(21) 12
25
1225
2
12212
25T
he n
ext
thre
e t
erm
s are
,
2,an
d
.1 } 8
1 } 4
1 } 2
1 } 8
1 } 2
1 } 4
1 } 4
1 } 2
1 } 2
1 } 2
1 } 2
1 } 2
24
}8
b.
7,
14,
28,
56,
…
Th
e c
om
mon
rati
o i
s or
2.U
se t
his
info
rmati
on
to f
ind
th
e n
ext
thre
e t
erm
s.
56(2
) 5
112
112(2
) 5
224
224(2
) 5
448
Th
e n
ext
thre
e t
erm
s are
112,224,448.
14
}7
Fin
d t
he n
ex
t th
ree t
erm
s i
n e
ach
geo
metr
ic s
eq
uen
ce.
©G
lencoe/M
cG
raw
-Hill
616
Gle
ncoe A
lgebra
1
Geo
metr
ic M
ean
sA
mis
sin
g t
erm
or
term
s betw
een
tw
o n
on
con
secu
tive t
erm
s in
ageom
etr
ic s
equ
en
ce a
re c
all
ed
geo
metr
ic m
ea
ns.In
th
e s
equ
en
ce 1
0,20,40,80,…
,th
egeom
etr
ic m
ean
betw
een
10 a
nd
40 i
s 20.Y
ou
can
use
th
e f
orm
ula
an
5a
1?
rn2
1to
fin
d a
geom
etr
ic m
ean
. Fin
d t
he g
eo
metr
ic m
ea
n i
n t
he s
eq
uen
ce 6
,,
150.
In t
he s
equ
en
ce,a
1=
6 a
nd
a3
= 1
50.T
o f
ind
a2,you
mu
st f
irst
fin
d r
.
an
5a
1?
rn2
1F
orm
ula
for
the n
th t
erm
of
a g
eom
etr
ic s
equence
a3
5a
1?
r3 2
1n
53
150
56 ?
r2a
35
150 a
nd a
15
6
5D
ivid
e e
ach s
ide b
y 6
.
25
5r2
Sim
plif
y.
65
5r
Take t
he s
quare
root
of
each s
ide.
If r
55,th
e g
eom
etr
ic m
ean
is
6(5
) or
30.If
r5
25,th
e g
eom
etr
ic m
ean
is
6(2
5)
or
230.
Th
ere
fore
th
e g
eom
etr
ic m
ean
is
30 o
r 2
30.
Fin
d t
he g
eo
metr
ic m
ea
ns i
n e
ach
seq
uen
ce.
1.
4,
,16
2.
12,
,108
3.
28,
,2
128
68
636
632
4.
180,
,20
5.
22,
,2
98
6.
600,
,150
660
614
6300
7.
,,
8.
,,
9.
2,
,2
66
6
10.14,
,11.
,,10
12.
2,
,2
54
62
66
6
13.2.3
,,9.2
14.
2137.7
,,
215.3
15.
25.1
,,
2127.5
64.6
645.9
625.5
16.
,,
17.
215,
,2
18.
8,
,320,0
00
66
36
1600
3} 1
6
3 } 5
3} 3
2
3 } 8
5 } 2
2 } 3
5 } 8
2 } 7
3 } 4
1 } 8
1 } 8
15
} 16
3 } 5
1} 3
2
1 } 2
1} 1
6
1 } 4
6r2
}6
150
}6
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued)
Geo
metr
ic S
eq
uen
ces
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D__
___
10-7
10-7
Example
Example
Exercises
Exercises
Answers (Lesson 10-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swers
Skil
ls P
racti
ce
Geo
metr
ic S
eq
uen
ces
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-7
10-7
©G
lencoe/M
cG
raw
-Hill
617
Gle
ncoe A
lgebra
1
Lesson 10-7
Dete
rm
ine w
heth
er e
ach
seq
uen
ce i
s g
eo
metr
ic.
1.
9,17,25,33,…
no
2.
4,12,36,108,…
ye
s
3.
2320,
280,
220,
25,…
ye
s4.
275,
260,
245,
230,…
no
5.
64,
232,16,
28,…
ye
s6.
26.5
,21,15.5
,10,…
no
Fin
d t
he n
ex
t th
ree t
erm
s in
ea
ch
geo
metr
ic s
eq
uen
ce.
7.
2,
24,8,
216,…
8.
22,
26,
218,
254,…
32,
264,128
2162,
2486,
21
45
8
9.
2960,480,
2240,120,…
10.
7290,2430,810,270,…
260,30,
215
90,30,10
11.
232,
216,
28,
24,…
12.
6144,1536,384,96,…
22,
21,
20.5
24,6,1.5
Fin
d t
he n
th t
erm
of
ea
ch
geo
metr
ic s
eq
uen
ce.
13.a
15
2,n
54,r
52
22
16
14.
a1
53,n
55,r
52
48
15.a
15
6,n
53,r
58
38
416.
a1
52
5,n
54,r
59
23
64
5
17.a
15
10,n
53,r
512
14
40
18.
a1
54,n
54,r
52
82
20
48
Fin
d t
he g
eo
metr
ic m
ea
ns
in e
ach
seq
uen
ce.
19.8,
,72
62
420.
75,
,3
61
5
21.
22,
,2
128
61
622.
2112,
,2
76
28
23.324,
,4
63
624.
1.5
,,24
66
©G
lencoe/M
cG
raw
-Hill
618
Gle
ncoe A
lgebra
1
Dete
rm
ine w
heth
er e
ach
seq
uen
ce i
s g
eo
metr
ic.
1.
3,12,48,192,…
ye
s2.
2,17,32,47,…
no
3.
2200,
2135,
270,
25,…
no
4.
2220,
2110,
255,
227.5
,…
ye
s
5.
2992,248,
262,15.5
,…
ye
s6.
220,
250,
2125,
2312.5
,…
ye
s
Fin
d t
he n
ex
t th
ree t
erm
s in
ea
ch
geo
metr
ic s
eq
uen
ce.
7.
24,
220,
2100,
2500,…
8.
7,
221,63,
2189,…
22500,
212,5
00,
262,5
00
567,
21701,5103
9.
26250,1250,
2250,50 …
10.
50,70,98,137.2
,…
210,2,
20.4
192.0
8,268.9
12,376.4
768
11.5,
24,3.2
,2
2.5
6 …
12.
,,
,,…
2.0
48,
21.6
384,1.3
1072
,,
Fin
d t
he n
th t
erm
of
ea
ch
geo
metr
ic s
eq
uen
ce.
13.a
15
6,n
55,r
53
14.
a1
52
9,n
56,r
52
15.
a1
58,n
53,r
52
11
48
62
28
89
68
16.a
15
50,n
57,r
53
17.
a1
52
5,n
53,r
51.5
18.
a1
57,n
55,r
50.5
36,4
50
211.2
50.4
375
Fin
d t
he g
eo
metr
ic m
ea
ns
in e
ach
seq
uen
ce.
19.4,
,256
63
220.
28,
,2
392
65
621.
2,
,0.5
61
22.
220,
,2
1.2
56
523.
,,
624.
,,
6
MA
GA
ZIN
E S
UB
SC
RIP
TIO
NS
Fo
r E
xercis
es
25 a
nd
26,u
se t
he f
oll
ow
ing
in
form
ati
on
.
Th
e m
an
ager
of
a t
een
magazi
ne
wan
ts t
o in
crea
se s
ubsc
rip
tion
s by a
t le
ast
6%
each
yea
rfo
r th
e n
ext
thre
e yea
rs t
o k
eep
th
e co
mp
an
y o
per
ati
ng a
t a p
rofi
t.S
ubsc
rip
tion
s fo
r 2003
are
17,5
00.
25.D
eter
min
e th
e m
inim
um
nu
mber
of
subsc
rip
tion
s th
e sa
les
team
mu
st s
ell
for
the
yea
rs2004,2005,an
d 2
006.
18,5
50;
19,6
63;
20,8
43
26.S
up
pos
e th
e m
an
ager
wan
ts t
o in
crea
se t
he
subsc
rip
tion
s to
35,0
00.H
ow l
ong w
ill
itta
ke
to r
each
th
is g
oal
if s
ubsc
rip
tion
s in
crea
se a
t 6%
per
yea
r?ab
ou
t 12 y
r1 } 52
} 25
1 } 2
3 } 16
3} 6
43 } 4
16
} 729
8} 2
43
4 } 81
2} 2
71 } 9
1 } 61 } 4
Pra
cti
ce (
Avera
ge)
Geo
metr
ic S
eq
uen
ces
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-7
10-7
Answers (Lesson 10-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
cs
Geo
metr
ic S
eq
uen
ces
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D_____
10-7
10-7
©G
lencoe/M
cG
raw
-Hill
619
Gle
ncoe A
lgebra
1
Lesson 10-7
Pre
-Act
ivit
yH
ow
ca
n a
geo
metr
ic s
eq
uen
ce b
e u
sed
to
desc
rib
e a
bu
ng
ee j
um
p?
Read
th
e i
ntr
od
uct
ion
to L
ess
on
10-7
at
the t
op
of
page 5
67 i
n y
ou
r te
xtb
ook
.
How
can
you
fin
d t
he d
ista
nce
of
the f
ifth
bou
nce
?
Mu
ltip
ly 3
3ft
by
.
Read
ing
th
e L
ess
on
1.
Su
pp
ose
you
are
giv
en
th
e f
irst
th
ree t
erm
s of
a g
eom
etr
ic s
equ
en
ce a
nd
wan
t to
fin
d t
he
next
thre
e t
erm
s.
a.
Wh
at
shou
ld y
ou
do t
o f
ind
th
e c
om
mon
rati
o?
Div
ide t
he s
eco
nd
term
of
the s
eq
uen
ce b
y t
he f
irst,
or
div
ide t
he t
hir
dte
rm b
y t
he s
eco
nd
.
b.
Wh
at
shou
ld y
ou
do a
fter
you
fin
d t
he c
om
mon
rati
o?
Beg
inn
ing
wit
h t
he t
hir
d t
erm
of
the s
eq
uen
ce
,m
ult
iply
by t
he
co
mm
on
rati
o.M
ult
iply
th
e r
esu
ltin
g p
rod
uct
by t
he c
om
mo
n r
ati
o,an
dre
peat
this
ste
p w
ith
th
e n
ew
pro
du
ct.
2.
Su
pp
ose
you
are
ask
ed
to g
ive a
n e
xam
ple
of
a g
eom
etr
ic s
equ
en
ce.A
re t
here
an
yre
stri
ctio
ns
on
th
e t
erm
s of
the s
equ
en
ce o
r th
e c
om
mon
rati
o r
? E
xp
lain
.
Yes;
the s
eq
uen
ce c
an
no
t b
eg
in w
ith
0,an
d t
he c
om
mo
n r
ati
o c
an
no
t b
eeq
ual
to 0
or
1.
3.
You
can
use
th
e f
orm
ula
for
the n
th t
erm
of
a g
eom
etr
ic s
equ
en
ce t
o f
ind
an
y t
erm
in
th
ese
qu
en
ce.W
hat
info
rmati
on
do y
ou
need
in
ord
er
to u
se t
he f
orm
ula
?
Yo
u n
eed
to
kn
ow
th
e f
irst
term
of
the s
eq
uen
ce
,th
e c
om
mo
n r
ati
o,an
dw
here
th
e t
erm
yo
u a
re i
nte
reste
d i
n f
alls i
n t
he s
eq
uen
ce
.
4.
Con
sid
er
the g
eom
etr
ic s
equ
en
ce 3
,6,12,24,48,…
.H
ow
man
y g
eom
etr
ic m
ean
s are
there
for
each
pair
of
term
s? W
hat
are
th
ey?
a.
3 a
nd
12
on
e;
6b
.3 a
nd
24
two
;6 a
nd
12
Help
ing
Yo
u R
em
em
ber
5.
To r
em
em
ber
an
id
ea,it
can
help
if
you
exp
lain
it
to s
om
eon
e e
lse.S
up
pose
a f
rien
dth
ink
s th
at
the f
orm
ula
for
the n
th t
erm
of
a g
eom
etr
ic s
equ
en
ce s
hou
ld b
e a
n5
a1r
n
rath
er
than
an
5a
1rn
21.H
ow
wou
ld y
ou
exp
lain
wh
y i
t sh
ou
ld b
e a
n5
a1r
n2
1?
Sam
ple
an
sw
er:
Th
e s
eq
uen
ce s
tart
s w
ith
a1.T
he s
eco
nd
term
is
a2
5a
1r1
.Th
e t
hir
d t
erm
is a
35
a1r
2,an
d s
o o
n.T
he e
xp
on
en
t fo
r r
is o
ne
less t
han
th
e t
erm
nu
mb
er.
So
an
5a
1r
n2
1.
3 } 43 } 4
©G
lencoe/M
cG
raw
-Hill
620
Gle
ncoe A
lgebra
1
Co
nverg
en
ce
,D
iverg
en
ce
,an
d L
imit
s
Imagin
e t
hat
a r
un
ner
run
s a m
ile f
rom
poin
t A
to p
oin
t B
.B
ut,
this
is
not
an
ord
inary
race
! In
th
e f
irst
min
ute
,h
e r
un
s on
e-h
alf
mil
e,re
ach
ing p
oin
t C
.
In t
he n
ext
min
ute
,h
e c
overs
on
e-h
alf
th
e r
em
ain
ing d
ista
nce
,or
mil
e,
reach
ing p
oin
t D
.In
th
e n
ext
min
ute
he c
overs
on
e-h
alf
th
e r
em
ain
ing
dis
tan
ce,or
mil
e,re
ach
ing p
oin
t E
.
In t
his
str
an
ge r
ace
,th
e r
un
ner
ap
pro
ach
es
close
r an
d c
lose
r to
poin
t B
,bu
t n
ever
gets
th
ere
.H
ow
ever
close
he i
s to
B,th
ere
is
stil
l so
me d
ista
nce
re
main
ing,an
d i
n t
he n
ext
min
ute
he c
an
cover
on
ly h
alf
of
that
dis
tan
ce.
Th
is r
ace
can
be m
od
ele
d b
y t
he i
nfi
nit
e s
equ
en
ce
,,
,,…
.
Th
e t
erm
s of
the s
equ
en
ce g
et
close
r an
d c
lose
r to
1.A
n i
nfi
nit
e s
equ
en
ce
that
gets
arb
itra
rily
clo
se t
o s
om
e n
um
ber
is s
aid
to c
on
verg
eto
th
at
nu
mber.
Th
e n
um
ber
is t
he l
imit
of
the s
equ
en
ce.
Not
all
in
fin
ite s
equ
en
ces
con
verg
e.T
hose
th
at
do n
ot
are
call
ed
div
erg
en
t.
Writ
e C
if
the s
eq
uen
ce c
on
verg
es
an
d D
if
it d
iverg
es.
If t
he
seq
uen
ce c
on
verg
es,
ma
ke a
rea
son
ab
le g
uess
fo
r i
ts l
imit
.
1.
2,4,6,8,10,…
D2.
0,3,0,3,0,3,…
D
3.
1,
,,
,,…
C,0
4.
0.9
,0.9
9,0.9
99,0.9
999,…
C,1
5.
25,5,
25,5,
25,5,…
D6.
0.1
,0.2
,0.3
,0.4
,…
D
7.
2,2
,2
,2
,…
C,3
8.
6,5
,5
,5
,5
,…
C,5
9.
1,4,9,16,25,…
D10.
21,
2,
2,
2,
2,…
C,0
11.C
reate
on
e c
on
verg
en
t se
qu
en
ce a
nd
on
e d
iverg
en
t se
qu
en
ce.G
ive t
he
lim
it f
or
you
r co
nverg
en
t se
qu
en
ce.
An
sw
ers
will
vary
.S
am
ple
an
sw
er:
1,
,,
,,…
co
nverg
en
t,0
1,5,25,125,625,…
div
erg
en
t
1} 8
11
} 27
1 } 91 } 3
1 } 5
1 } 4
1 } 3
1 } 2
1 } 5
1 } 4
1 } 3
1 } 2
15
} 16
7 } 8
3 } 4
1 } 4
1 } 5
1 } 4
1 } 3
1 } 2
15
} 16
7 } 8
3 } 4
1 } 2
D(3
:02 P
.M.)
C(3
:01 P
.M.)
B (?)
E(3
:03 P
.M.)
A(3
:00 P
.M.)
0 m
ilem
ile1 – 2
mile
3 – 4m
ile7 – 8
1 m
ile
1 } 8
1 } 4
En
rich
men
t
NA
ME
______________________________________________
DA
TE
____________
PE
RIO
D__
___
10-7
10-7
Answers (Lesson 10-7)