Warm Up4

2

-2

-4

5

Identify the Roots and the Zeros of this quadratic.

Solving Quadratics by Factoring

• To “solve” a quadratic means to find the roots.

• Easy when you have a graph (just look at the points where it crosses the x-axis)

• But we will solve just from the equation

3 Steps to Solve quadratics

1. Set equation equal to zero2. Factor3. Set each factor equal to 0 and solve

Example 1

Step 1: Rearrange the terms to have zero on one side:

2 22 15 2 15 0x x x x

Continued…

Step 2: Factor

(x+5)(x-3)

Continued

So the roots are x = -5 or x = 3

Step 3:Set each factor equal to zero and solve:

( 5) 0 and ( 3) 0

5 3

x x

x x

Factors, Roots, Zeros

y x2 2x 15For our Polynomial Function:

The Factors are: (x + 5) & (x - 3)

The Roots/Solutions are: x = -5 and 3

The Zeros are at: (-5, 0) and (3, 0)

• What do you notice about the relationship between factors and solutions?

• All you have to do is switch the sign!

• If the factor is (x+1) then the solution is -1.Easy!

Example 2

𝑎2− 2𝑎=−1

• Factors are (x+2)(x-1)

• Solutions/roots are -2 and 1

• Zeros are (-2,0) and (1,0)

You try!

Solutions are -5 and -3

Homework