Warm Up 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 zero 2.Factor 3.Set each factor equal to 0 and solve

Example 1

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:

Factors, Roots, Zeros For 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 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