Solving Quadratic Equations

Before we learn to solve quadratic equations, we need to remember an important property!

Zero Product Property

Examples:

If ab = 0, then a = 0 or b = 0.

a and b are real numbers (“factors”)

a2= 0, then a = 0

3b = 0 then b = 0a(a + 2) = 0, then a = 0 or a +2 = 0 SO…a = 0 or a = -2.

Solving Quadratics

Let’s learn how to solve quadratics by factoring the greatest common

factor!

When solving by factoring the GCF, the quadratic equation will look a certain way!

The quadratic equation will have two types of terms: A quadratic term and a linear term. 02 bxax

Examples

ww 24 2 035 2 tt

OK, so how do we solve quadratic equations that look this way?!!!

Solve by factoring GCFww 24 2

0

02

w

w

024 2 ww

0)12(2 ww

2

1

012

w

w

Solve

Step 1: Make one side zero, if not already.

Step 2: Factor out the GCF.

Step 3: Set each factor to zero and solve for the variable.

OR

Let’s Practice!

You Try It!

0)35( tt

035 2 ttSolve

035or 0 ttFactor the

GCF!5

3or 0 tt

YOU DID IT!Hooray!!!

THE END