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