1. 5-5: Quadratic Equations
Essential Question:
How is factoring used to solve quadratic equations?

2. 5-5: Quadratic Equations
The standard form of a quadratic equation is:
ax2 + bx + c = 0
We can solve some quadratic equations by factoring
We’ll solve non-factorable equations after we come back from break
We solve a factored quadratic equation because of the Zero-Product Property
If ab = 0, then a = 0 or b = 0
Example: If (x + 3)(x – 7) = 0, then x = -3 or x = 7
Take each parenthesis, set it equal to 0 and solve for x

3. 5-5: Quadratic Equations
Solve by factoring
2x2 – 11x = -15
Get everything equal to 0 (add 15 to both sides)
2x2 – 11x + 15 = 0
Last step: Set each parenthesis = 0 and solve (next slide) +
2 numbers to:
multiply = 30
add = -11
-5 & -6
2x2 x x + 15 -5 -6
x(2x - 5)
-3(2x - 5)
(x - 3)(2x - 5)

4. 5-5: Quadratic Equations
x – 3 = x = 3
2x – 5 = 0
x = 5 2 2 x = 5/2
Optionally: Check your answers
2x2 – 11x + 15 = 0
2(3)2 – 11(3) + 15 = 0
18 – = 0
0 = 0
2(5/2)2 – 11(5/2) + 15 = 0
25/2 – 55/ = 0

5. 5-5: Quadratic Equations
Solve each equation by factoring
x2 + 7x = 18
2x2 + 4x = 6
16x2 = 8x
x = 2 or x = -9
x = 1 or x = -3
x = 0 or x = ½

6. 5-5: Quadratic Equations
Assignment
Page 270
1 – 10 (all problems)
Solve all problems by factoring (not square roots)
No work = no credit