1. Solving Quadratic Equations by Factoring
Skill 57

2. Objective
HSA-REI.4.b: Solve quadratic equations by graphing or factoring.

3. A zero of a function is a value of the x that makes the f(x) equal zero. The zeros of a function are the x-intercepts.

4. The solution to a quadratic equation of the form
ax2 + bx + c = 0 are roots. The roots of an equation are the values of the variable that make the equation true.
You can find the roots of some quadratic equations by factoring and applying the Zero Product Property.

5. Example: Finding Zeros by Factoring
Find the zeros of the function by factoring.
f(x) = x2 + 3x – 28
x2 + 3x – 28 = 0
Set the function equal to 0.
(x + 4)(x – 7) = 0
Factor: Find factors of –12 that add to –4.
x + 4 = 0 or x – 7 = 0
Apply the Zero Product Property.
x= –4 or x = 7
Solve each equation.

6. Do It Yourself: Example
Find the zeros of the function by factoring.
f(x)= x2 – 7x + 6
x2 – 7x + 6 = 0
Set the function equal to 0.
(x - 1)(x – 6) = 0
Factor: Find factors of –6 that add to –5.
x - 1 = 0 or x – 6 = 0
Apply the Zero Product Property.
x = 1 or x = 6
Solve each equation.

7. Do It Yourself: Example
Find the zeros of the function by factoring.
g(x) = x2 – 8x
x2 – 8x = 0
Set the function to equal to 0.
x(x – 8) = 0
Factor: The GCF is x.
x = 0 or x – 8 = 0
Apply the Zero Product Property.
x = 0 or x = 8
Solve each equation.

8. 57: Solving Quadratic Equations by Factoring
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