1. Completing the Square

2. Table of Contents
46: Warm-Up, Guided Practice, Reflection
47: How Do I Factor Quadratics by Completing the Square?

3. Warm-Up
Solve for x: 1. 4x2 – 36 = x2 – 720 = 0 Factor the following: 3. x2 – 8x – 9 = x2 + 8x – 9 = 0

4. Warm-Up Answers
Solve for x: 1. 4x2 – 36 = x2 – 720 = 0 Factor the following: 3. x2 – 8x – 9 = x2 + 8x – 9 = 0
x = 3 and -3
x = 12 and -12
(x – 9)(x + 1)
(x + 9)(x – 1)

5. Learning Intention/Success Criteria
LI: We are learning to factor quadratics by completing the square SC: I know how to -take the square root of values -solve for the roots -explain why completed square form is also known as vertex form -solve quadratic equations by completing the square -divide and add integers -simplify equations and expressions -factor quadratics using stick man

6. EQ: How Do I Factor Quadratics Using Completing the Square?
11/19/2018

7. Vertex Form
F(x) = a(x – h)2 + k
Also known as completed square form
Vertex: (h, k)

8. Example 1: List the vertex of the equation
h(x) = -4(x – 5)2 + 9
(5, 9)

9. Guided Practice 1
Find the vertex of the following equation: f(x) = 2(x + 6)2 – 8

10. Guided Practice 1
Find the vertex of the following equation: f(x) = 2(x + 6)2 – 8
A] (6, 8)
B] (6, - 8)
C] (-6, -8)
D] (-6, 8)

11. Guided Practice 2
Find the vertex of the following equation: d(x) = 7(x – 12)2 – 3

12. Guided Practice 2
Find the vertex of the following equation: d(x) = 7(x – 12)2 – 3
A] (12, 3)
B] (12, - 3)
C] (-12, -3)
D] (-12, 3)

13. Guided Practice 3
Find the vertex of the following equation: j(x) = -3(x + 8)2 + 5

14. Guided Practice 3
Find the vertex of the following equation: j(x) = -3(x + 8)2 + 5
A] (8, 5)
B] (8, - 5)
C] (-8, -5)
D] (-8, 5)

15. Foldable Video

16. Example 2: Solve for x by completing the square x2 + 4x – 1 = 0
______________
+ 1
+ 1
x2 + 4x = 1
𝐵 2 2 = 3
= 2 2
= 4
x2 + 4x + 4 = 1 + 4 4
x2 + 4x + 4 = 5 5
(x + 2)2 = 5 6
(x + 2)2 = 5 7
𝑥+2= ± 5 8
𝑥=−2± 5

17. Guided Practice 4
Solve for x by completing the square: x2 + 8x – 3 = 0

18. Guided Practice 4
Solve for x by completing the square: x2 + 8x – 3 = 0
A] x =  1
B] x = -4  3
C] x = 0
D] x = -4  19

19. Guided Practice 4
Solve for x by completing the square: x2 + 8x – 3 = 0
𝐵 2 2 =
= 4 2
= 16
+ 3
+ 3
________________
x2 + 8x = 3
________________
+ 16
+ 16
x2 + 8x + 16 = 19
(x + 4)2 =
x + 4 = ± 19
________________
- 4
- 4
x = - 4 ± 19

20. Guided Practice 5
Solve for x by completing the square: x2 + 24x + 32 = 0

21. Guided Practice 5
Solve for x by completing the square: x2 + 24x + 32 = 0
A] −12 ±4 7
B] 12 ±4 7
C] −12 ±4 11
D] 12 ±4 11

22. Guided Practice 4
Solve for x by completing the square: x2 + 24x + 32 = 0 =
𝐵 2 2
= 12 2
= 144
________________
-32
-32
x2 + 24x = -32
x = -12 ± 16∗7
________________
+ 144
+ 144
x = -12 ±4 7
x2 + 24x +144 = 112
(x + 12)2 = 112
x + 12 = ± 112
________________
- 12
- 12
x = -12 ± 112

23. Example 2: Solve for x by completing the square
4x2 + 16x – 9 = 0
4x2 + 16x – 9 = 0
___ 4
___ 4
___ 4
x2 + 4x – 𝟗 𝟒 = 0
+ 𝟗 𝟒
+ 𝟗 𝟒
_________________
x2 + 4x = 𝟗 𝟒
= 𝟒 𝟐 𝟐
𝑩 𝟐 𝟐
= 𝟐 𝟐
= 4
x2 + 4x = 𝟗 𝟒
_________________
+ 4
+ 4
x2 + 4x + 4 = 𝟗 𝟒 + 𝟏𝟔 𝟒

24. x2 + 4x + 4 = 𝟐𝟓 𝟒
(x + 2)2 = 𝟐𝟓 𝟒
x =  𝟓 𝟐
_________________
- 2
- 2
x = -2  𝟓 𝟐
x = 𝟓 𝟐 x = 𝟓 𝟐
x = 1/2
x = -4.5

25. Guided Practice 6
Solve for x by completing the square: 7x2 + 28x – 49 = 0

26. Poll Solve for x by completing the square: x2 + 24x + 32 = 0 A] −2 ± 3
D] −2 ± 11

27. Guided Practice 6
Solve for x by completing the square: 7x2 + 28x – 49 = 0
___ 7
___ 7
___ 7 =
𝐵 2 2
= 2 2
= 4
x2 + 4x – 7 = 0
______________
+ 7
+ 7
(x + 2)2 = 11
x2 + 4x = 7
x + 2 = ± 11
+ 4
+ 4
______________
- 2
- 2
x2 + 4x + 4 = 11
x = −2 ± 11
(x + 2)2 = 11