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