SWBAT: solve quadratic equations using the quadratic formula.

SWBAT: solve quadratic equations using the quadratic formula.

x2 + 8x + y2 – 4y = -14

Magic number for x: 𝟖

𝟐

𝟐= 𝟏𝟔

Magic number for y: −𝟒

𝟐

𝟐= 𝟒

(x + 4)2 + (y - 2)2 = 6 Center = (-4, 2)

r = 𝟔 ≈ 𝟐. 𝟒

x2 + 8x + 16 + y2 – 4y + 4 = -14 + 16 + 4

SWBAT: solve quadratic equations using the quadratic formula.

2 ax2 + bx + c = 0

0

Factoring

decimal 𝒏𝒐𝒏 − 𝒑𝒆𝒓𝒇𝒆𝒄𝒕 𝒔𝒒𝒖𝒂𝒓𝒆 #

−𝒃 ± 𝒃𝟐 − 𝟒𝒂𝒄

𝟐𝒂

SWBAT: solve quadratic equations using the quadratic formula.

No 2x2 - 4x - 1 = 0

2 -4 -1

x = − ± ( )𝟐−𝟒( )( )

𝟐( )

x = − −𝟒 ± (−𝟒)𝟐−𝟒(𝟐)(−𝟏)

𝟐(𝟐)

x = 𝟒 ± 𝟐𝟒

𝟒

𝟒 ± 𝟒 𝟔

𝟒

x = 𝟒 ± 𝟐 𝟔

𝟒

GCF = 2 Divide all whole numbers by 2

x = 𝟐 ± 𝟔

𝟐

SWBAT: solve quadratic equations using the quadratic formula.

SWBAT: solve quadratic equations using the quadratic formula.

3x2 + 12x - 3 = 0

a =

b =

c =

3

12

-3

x = − ± ( )𝟐−𝟒( )( )

𝟐( )

x = − 𝟏𝟐 ± (𝟏𝟐)𝟐−𝟒(𝟑)(−𝟑)

𝟐(𝟑)

x = −𝟏𝟐 ± 𝟏𝟖𝟎

𝟔

−𝟏𝟐 ± 𝟑𝟔 𝟓

𝟔

x = −𝟏𝟐 ± 𝟔 𝟓

𝟔

x = -2 ± 𝟓

GCF = 6 Divide all whole numbers by 6

SWBAT: solve quadratic equations using the quadratic formula.

x2 - 6x - 12 = 0

a =

b =

c =

1

-6

-12

x = − ± ( )𝟐−𝟒( )( )

𝟐( )

x = − −𝟔 ± (−𝟔)𝟐−𝟒(𝟏)(−𝟏𝟐)

𝟐(𝟏)

x = 𝟔 ± 𝟖𝟒

𝟐

𝟔 ± 𝟒 𝟐𝟏

𝟐

x = 𝟔 ± 𝟐 𝟐𝟏

𝟐

x = 3 ± 𝟐𝟏

GCF = 2 Divide all whole numbers by 2

SWBAT: solve quadratic equations using the quadratic formula.

7x2 + 4x + 8 = 0

a =

b =

c =

7

4

8

x = − ± ( )𝟐−𝟒( )( )

𝟐( )

x = − 𝟒 ± (𝟒)𝟐−𝟒(𝟕)(𝟖)

𝟐(𝟕)

x = −𝟒 ± −𝟐𝟎𝟖

𝟏𝟒

No Real Solution

SWBAT: solve quadratic equations using the quadratic formula.

x2 + 3x - 4 = 0

a =

b =

c =

1

3

-4

x = − ± ( )𝟐−𝟒( )( )

𝟐( )

x = − 𝟑 ± (𝟑)𝟐−𝟒(𝟏)(−𝟒)

𝟐(𝟏)

x = −𝟑 ± 𝟐𝟓

𝟐

−𝟑 ± 𝟓

𝟐

x = −𝟑 − 𝟓

𝟐 or x =

−𝟑 + 𝟓

𝟐 {-4, 1}

x = −𝟖

𝟐 or x =

𝟐

𝟐

SWBAT: solve quadratic equations using the quadratic formula.

SWBAT: solve quadratic equations using the quadratic formula.

–12t2 + 54t = 0

a =

b =

c =

-12

54

0

t = − ± ( )𝟐−𝟒( )( )

𝟐( )

t = − 𝟓𝟒 ± (𝟓𝟒)𝟐−𝟒(−𝟏𝟐)(𝟎)

𝟐(−𝟏𝟐)

t = −𝟓𝟒 ± 𝟐𝟗𝟏𝟔

−𝟐𝟒

−𝟓𝟒 ± 𝟓𝟒

−𝟐𝟒

t = −𝟓𝟒 − 𝟓𝟒

−𝟐𝟒 or t =

−𝟓𝟒 + 𝟓𝟒

−𝟐𝟒

t = −𝟏𝟎𝟖

−𝟐𝟒 or t =

𝟎

−𝟐𝟒

t = 4.5 sec

SWBAT: solve quadratic equations using the quadratic formula.

a =

b =

c =

-5

-8

120

t = − ± ( )𝟐−𝟒( )( )

𝟐( )

t = − −𝟖 ± (−𝟖)𝟐−𝟒(−𝟓)(𝟏𝟐𝟎)

𝟐(−𝟓)

t = 𝟖 ± 𝟐𝟒𝟔𝟒

−𝟏𝟎

𝟖 ± 𝟒𝟗.𝟔𝟑𝟖𝟕…

−𝟏𝟎

t = 𝟖 −𝟒𝟗.𝟔𝟑𝟖𝟕…

−𝟏𝟎 or t =

𝟖 + 𝟒𝟗.𝟔𝟑𝟖𝟕…

−𝟏𝟎

t 𝟒. 𝟐 𝒔𝒆𝒄 or t −𝟓. 𝟖 𝒔𝒆𝒄

SWBAT: solve quadratic equations using the quadratic formula.

a =

b =

c =

-16

200

0

Determine Maximum Height

x = -𝒃

𝟐𝒂 =

−( )

𝟐( )

= −( 𝟐𝟎𝟎)

𝟐(−𝟏𝟔)

t = −𝟐𝟎𝟎

−𝟑𝟐 =

𝟐𝟓

𝟒

𝑯𝒎𝒂𝒙 =-16(𝟐𝟓

𝟒)2 + 200(

𝟐𝟓

𝟒)

𝑯𝒎𝒂𝒙 = 625 ft

𝟔𝟐𝟓 > 𝟔𝟏𝟐; 𝒀𝒆𝒔 𝒉𝒆 𝒘𝒊𝒍𝒍!

SWBAT: solve quadratic equations using the quadratic formula.

a =

b =

c =

-4.9

68.6

0

Determine Maximum Height

x = -𝒃

𝟐𝒂 =

−( )

𝟐( )

= −( 𝟔𝟖.𝟔)

𝟐(−𝟒.𝟗)

t = −𝟔𝟖.𝟔

−𝟗.𝟖= 𝟕

𝑯𝒎𝒂𝒙 =-4.9(𝟕)2 + 68.6(𝟕)

𝑯𝒎𝒂𝒙 ≈ 240 meters

SWBAT: solve quadratic equations using the quadratic formula.

SWBAT: solve quadratic equations using the quadratic formula.

5a2 – 2a – 22 = 0 a =

b =

c =

5

-2

-22

a = − −𝟐 ± (−𝟐)𝟐−𝟒(𝟓)(−𝟐𝟐)

𝟐(𝟓)

a = 𝟐 ± 𝟒𝟒𝟒

𝟏𝟎

𝟐 ± 𝟒 𝟏𝟏𝟏

𝟏𝟎

a = 𝟐 ± 𝟐 𝟏𝟏𝟏

𝟏𝟎 GCF = 2 Divide all whole

numbers by 2

a = 𝟏 ± 𝟏𝟏𝟏

𝟓