Page 670 - Algebra 1

L E S S O N Solving Quadratic Equations by Factoring 98
Warm Up
New Concepts
1. Vocabulary A is an x-value for the function where f (x) = 0. (89)
Factor.
2.x2 +3x-88
(72)
4.4x2 +28x+49 (83)
3.6x2 -7x-5 (75)
5.12x2 -27 (83)
A root of an equation is the solution to an equation. A quadratic equation can have zero, one, or two roots. The roots of a quadratic equation are the x-intercepts, or zeros, of the related quadratic function.
To find the roots of a quadratic equation, set the equation equal to 0. If the quadratic expression can be factored, the equation can be solved using the Zero Product Property.
Using the Zero Product Property
Solve.
(x - 4)(x + 5) = 0
SOLUTION
By the Zero Product Property, one or both of these factors must be equal to 0. To find the solutions, set each factor equal to zero and solve.
x - 4 = 0 x + 5 = 0 Set each factor equal to zero. x = 4 x = -5 Solve each equation for x.
Check Substituteeachsolutionintotheoriginalequationtoshowitistrue.
Math Language
The roots of a quadratic equation are the values of x that make
ax2 +bx+c=0.
Zero Product Property
If the product of two quantities equals zero, at least one of the quantities equals zero.
Example
1
Math Reasoning
Analyze What is the difference between a quadratic function and a quadratic equation?
Online Connection www.SaxonMathResources.com
(x-4)(x+5)= 0 (4-4)(4+5) 0 0 · 9 0
0=0 ✓ The solution set is {-5, 4}.
(x-4)(x+5)=0 (-5-4)(-5+5) 0 -9 · 0 0
0=0 ✓
Lesson 98 655