completing the square 4-6 day 1
DESCRIPTION
Completing the Square 4-6 Day 1. Today’s Objective: I can use the process of completing the square to solve or rewrite a quadratic equation. Solve by Finding Square Root. Solving Perfect Square Trinomials. Factor: Perfect Square Trinomial. Solve:. Solve:. Solve:. - PowerPoint PPT PresentationTRANSCRIPT
Warm UpSolve by Finding Square Root
4 𝑥2=364 𝑥2+10=46
𝑥2=9𝑥=±3
3 𝑥2−5=253 𝑥2=30𝑥2=10
𝑥=±√10
Completing the Square4-6
Today’s Objective:I can use the process of completing the square
to solve or rewrite a quadratic equation
𝑓 (𝑥)=𝑎(𝑥−h)2+𝑘Vertex Form:• Opens• up (a > 0)• down (a < 0)
• Vertex: (h, k)• Axis of symmetry:
Quadratic Function Forms: Review
x
y𝑓 (𝑥)=𝑎𝑥2+𝑏𝑥+𝑐
Standard Form• Opens• up (a > 0)• down (a < 0)
• y-intercept: (0, c)• Vertex: • Axis of symmetry:
x
y
Quadratic Function: Factored Form𝑓 (𝑥)=𝑎(𝑥−𝑟 1)(𝑥−𝑟2)
ZerosAttributes:• Opens: up (a > 0) or down (a < 0)• Zeros of the function = Roots
(x intercepts)(𝑟1 ,0) (𝑟 2,0)
Solve:
Factor:
Perfect Square Trinomial
Solving Perfect Square Trinomials𝑥2+10 𝑥+25(𝑥+5)(𝑥+5)
(𝑥+5)2
𝑥2+10 𝑥+25=36(𝑥+5)2=36𝑥+5=±6
𝑥+5=6 𝑥+5=−6𝑥=1 𝑥=−11
Solve: 𝑥2−14 𝑥+49=25(𝑥−7 )2=25𝑥−7=±5
𝑥−7=5 𝑥−7=−5𝑥=12 𝑥=2
Solve: 𝑥2+6 𝑥+9=11(𝑥+3)2=11𝑥+3=±√11𝑥=−3 ±√11
Creating Perfect Square Trinomialsby: Completing the square
?2 bxx bxx 22
2
b 2
2
bx
Creating Perfect Square Trinomialsby: Completing the square
xx 102 ?
xx 102 2
210
bxx 2 bxx 22
2
b 2
2
bx
25102 xx2)5( x
xx 62 ?
xx 62 2
26
962 xx2)3( x
Solve by Completing the Squarebxx 2 bxx 2
2
2
b 2
2
bx
0382 xx
382 xx 16 1613)4( 2 x134 x
134 x
Rewrite equation: cbxx 2
012182 xx
12182 xx 81 8169)9( 2 x699 x
699 x
Solve by Completing the Squarebxx 2 bxx 2
2
2
b 2
2
bx
03183 2 xx
162 xx 9 98)3( 2 x
83 x83x
3183 2 xx7332 2 xxx
222 xx 1 13)1( 2 x
31 x
442 2 xx
31x223x
p. 237:13–17 odd, 19-45 odd [Factor out
the 2.]
Completing the Square4-6Day 2
Today’s Objective:I can use the process of completing the square
to solve or rewrite a quadratic equation
Write quadratic functions in vertex form𝑦=𝑥2+4 𝑥−6
𝑥=−𝑏2𝑎
Vertex:
¿−42(1)¿−2
𝑦=(−2)2+4 (−2 )−6¿−10
𝑦=(𝑥+2)2−10
2
2
b
Writing quadratic functions in vertex formby: Completing the Square
bxx 2 bxx 22
2
bx
642 xxy
642 xxy 4 4
10)2( 2 xy
1162 xxy
1162 xxy 9 9
20)3( 2 xy
Writing equations in Vertex Formby: Completing the Square
bxx 2 bxx 22
2
b 2
2
bx
17243 2 xxy17)8(3 2 xxy 16 )16(3
31)4(3 2 xy WS Completing the Square