1. Solving Quadratic Equations by Factoring

2. Factor To Solve a Quadratic Equation
1. Set trinomial = 0 and factor
2. Set both binomials = 0 and solve them each for x

3. Quadratic Equation Solutions:
You could get two solutions, one solution, or no solutions
The solutions are the x intercepts of the function
Plugging in a 0 for the y (set the equation = 0) gives x intercepts

4. Zero-Product Property
States that if the product of two factors is zero then one (or both) of the factors must be zero.
If ab=0, then either a=0, b=0 or both=0

5. Solve Quadratic Equation
x2 -11x + 24 = 0
STEPS:
Factor and set=0
(x-8)(x-3)=0
Set both binomials =0 and solve each
x-8=0 or x-3=0
x-8=0
x-3=0
x=3
x=8
2 Solutions
x = 3, 8

6. When you find the “x” values, you are finding out where the parabola crosses the x-axis when you graph the quadratic equation.

7. Make sure your quadratic is in standard form set=0 before you start!
4x2=7x+2
Keep x2 positive
Factor
4x2-7x-2=0
(4x+1)(x-2)=0
Solve each for x
4x+1=0
x-2=0
4x=-1
x=2
x=-1/4
x=-1/4 , 2

8. (2x+ )(x- )=0 x = -2.5 x = 1 2x2+3x-5=0 (2x+5 )(x- 1 )=0 2x+5=0 x-1=0

9. Sometimes there is just one solution:
x2-6x+11=2
-2 -2
Perfect sq. tri.
x2-6x+9 = 0
(x-3)2=0
x-3=0
x = 3

10. Solve
4x2-18x=0
(2x)(2x-9)=0
2x=0
2x-9=0
2x=9
x=0