1. 9.5 Factoring to Solve Quadratic Equations
Objective: SWBAT solve a quadratic equation by factoring or completing the square.

2. Mini Quiz 26
1. Solve x = 8
2. Graph x2 + 4 = 0

3. Overview
So far…You’ve learned how to solve a quadratic equation by graphing
…by taking the square root (when b = 0) (square root method)
Today you will practice how to…
Solve Quadratic Equation
In factored form
By factoring
(x + 2)(x – 3) = 0

4. Solving Quadratic Equations by Factoring
Steps:
Set equal to 0 (ax2 + bx + c = 0)
Factor the polynomial ax2 + bx + c into ( )( )
Set each one ( ) = 0 (zero product property)
Solve for “x”

5. “0” Product Property (anything times “0” equals…“0”!)
Solve
(x + 2)(x – 3) = 0
x + 2 = 0
x = -2
x – 3 = 0
x = 3

6. Factor First! Solve x2 + 8x + 12 = 0 (x + 2) (x + 6) = 0 x + 2 = 0
Use Zero Product Property
x + 6 = 0
x = -6

7. Standard Form than Factor!
Solve 6y2 + 12y + 13 = 2y2 + 4
4y2 + 12y + 9 =0
(2x + 3) (2x + 3) = 0
2x + 3 = 0
2x = -3
x = -3 2
Use Zero Product Property
2x + 3 = 0
2x = -3
x = -3 2

8. Practice Problems Solve 6. x2 – 16x + 55 = 0 7. t2 – 3t = 28
8. 3q2 + 16q = -5
9. 4x2 = 25
x = 5, x = 11
x = -4, x = 7
x = -5, x = -1/3
x = -5/2, x = 5/2

9. Practice Problems Solve 10. x2 + 5x + 4 = 0 11. y2 – 15y = -26
12. 4 = -5n + 6n2
13. 4t = 10t + 3t2 – 4
x = -1, x = -4
x = 2, x = 13
x = -1/2, x = 4/3
x = 4, x = 6

10. Wrap Up Solving Quadratic Equations Set = 0 Factor into ( )( ) ( ) = 0
( ) = 0
Solve for “x”
HW: P #1-21 odd, odd, 60
DLUQ: What kind of form does an equation need to be in order to use the “0” Product Property