1. Homework Review

2. Do Now: Level 1 Factor each quadratic function and determine the zeros if possible
a. f(x) = x2 + 5x + 4
b. f(x) = x2 - 4x + 2 4
(x + 1)(x + 4) = 0 2
Not Factorable 1 4  
x + 1 = 0 5 -4
x = -1
c. Approximate √10
x + 4 = 0
x = -4
3.2

3. Do Now: Level 2 d. f(x) = 2x2 + 10x + 4 e. f(x) = 3x2 - 12x - 15-5
(x - 5)(x + 1) = 0 2 -5 1  
x - 5 = 0 -4 5
x = 5
Not Factorable
x + 1 = 0
x = - 1

4. Do Now Level 2
f. Approximate √40
6.4

5. 13.7 Completing the Square
SWBAT solve quadratic equations by completing the perfect square Trinomial.

6. If you cannot factor a quadratic function, does that mean it does not have zeros? Explain
No.​The​functions​in​parts​(b)​and​(c)​cannot​be​factored​because​no​factors​of​the​ “c” value​can​add to get the “b” value. The functions might have zeros.

7. GRAPH AND SEE
b. f(x) = x2 - 4x + 2 x -1 1 2 4 y 7 -2

8. GRAPH AND SEE
d. f(x) = x2 + 5x + 2 x -5 -4 -3 -2 y 2

9. Factor Perfect Square Trinomials
Perfect Square Trinomial: Perfect Square Trinomials have first and last terms that are positive perfect squares. And the middle term is twice the product of the square roots of the first and third terms.
x2 + 4x + 4 4
(x + 2)(x + 2) 2 2 4
(x + 2)2

10. Factor Perfect Square Trinomials
n2 + 8n + 16 16
(n + 4)(n + 4) 4 4 8
(n + 4)2

11. Solving by Factoring Perfect Square Trinomials
exact
approximate
(x+2)(x+2)=5
(n+4)(n+4)=6 4 2 16 8 4
(x+2)2 =5
(n+4)2 =6
√(x+2)2 =±√5
√(n+4)2 =±√6
x+2 =±√5
n+4 =±√6
x = -2 ±√5
n = -4 ±√6
n = -4 +√6
n = -4 -√6
n =
n =
n = -1.5
n = - 6.5

12. Factor and Solve Perfect Square Trinomials
(p-5)(p-5)=9 81 18 9
(g+9)(g+9)=17 25
-10 -5
(g+9)2 =17
(p-5)2 =9
√(g+9)2 =±√17
√(p-5)2 =±√9
g+9 =±√17
p-5 =±3
g = -9 ±√17
p = 5 ±3
g = -9 +√17
g = -9 -√17
p = 5 +3
p = 5 -3
g =
g = -9 – 4.2
p = 8
p = 2
g =
g = -4.8

13. Before factoring, how can you tell if a trinomial is a square trinomial?
Before factoring, I can tell if a trinomial is a square trinomial by checking for:
First term is a positive perfect square
Last term is a positive perfect square
The middle term is twice the product of the square root of the first term and the square root of the third term.
What should a square trinomial look like when factored?
After factoring the trinomial you should have the same factors. This means that you will have the same quantity squared.

14. COMPLETING THE PERFECT SQUARE “TRINOMIAL”
If a ≠ 1, divide each term by that value to create a = 1
x2 - 4x + 2 = 0
Move the constant to the right hand side by adding or subtracting
x2 - 4x = -2
Complete the square trinomial:
Find and add it to both sides in order to complete the square and balance the equation
x2 - 4x + 4 = -2 +4

15. COMPLETING THE SQUARE “TRINOMIAL”
x2 - 4x + 4 = 2
Factor the square trinomial.
(x – 2)(x – 2) = 2
(x – 2)2 = 2
Square root both sides
(don’t forget the +/-)
Simplify and solve

16. COMPLETING THE SQUARE “TRINOMIAL”
Check if a=1, if its not, divide each term by a.
Move the constant to the right.
Complete the Perfect Square by finding (b/2)2 and adding it to both sides of the equal sign.
Solve the completed square:
Factor the Perfect Square Trinomial.
Square root both sides
Simplify and solve
x2 - 6x + 6 = 0
x2 - 6x = -6
x2 - 6x + 9 =
x2 - 6x + 9 = 3
(x - 3)2 = 3
√(x - 3)2 = ±√3
x – 3 = ±√3
x = 3 ± √3

17. COMPLETING THE SQUARE “TRINOMIAL”
5x2 - 35x -40 = 0
Completing the square:
Check if a=1, if its not, divide each term by a.
Move the constant to the right.
Complete the Perfect Square by finding (b/2)2 and adding it to both sides of the equal sign.
Solve the completed square:
Factor the Perfect Square Trinomial.
Square root both sides
Simplify and solve
x2 - 7x -8 = 0
x2 - 7x = 8
x2 - 7x =
x2 - 6x = 20.25
(x – 3.5)2 = 20.25
√(x – 3.5)2 = ±√20.25
x – 3.5 = ±√20.25
x = 3.5 ± √20.25

18. Must complete: you choose order
Braingenie.ck12.org- Completing the Square
Skills Practice (#1-6)
13.7 Exit Slip on engradela.org