# Chapter 6 Quadratic Equations By Factoring Worksheet With Answer Key - Mcgraw-Hill

6.9
by Factoring
OBJECTIVES
6.9
1.
Solve a quadratic equation by factoring
2.
Find the zeros of a quadratic function
The factoring techniques you have learned provide us with tools for solving equations that
can be written in the form
This is a quadratic equation in one variable, here x.
You can recognize such a quadratic equation by
2
ax
bx
c
0
a
0
the fact that the highest power of the variable x is
the second power.
in which a, b, and c are constants.
2
An equation written in the form ax
bx
c
0 is called a quadratic equation in
standard form. Using factoring to solve quadratic equations requires the zero-product
rule, which says that if the product of two factors is 0, then one or both of the factors must
be equal to 0. In symbols:
Rules and Properties: Zero-Product Rule
If a b
0, then a
0 or b
0 or a
b
0.
Let’s see how the rule is applied to solving quadratic equations.
Example 1
Solving Equations by Factoring
Solve.
2
x
3x
18
0
Factoring on the left, we have
NOTE
(x
6)(x
3)
0
To use the zero-product
rule, 0 must be on one side of
the equation.
By the zero-product rule, we know that one or both of the factors must be zero. We can then
write
x
6
0
or
x
3
0
Solving each equation gives
NOTE
Graph the function
2
y
x
3x
18
x
6
or
x
3
The solutions to the equation
The two solutions are 6 and
3 and the solution set is written as x x
3, 6 or simply
2
0
x
3x
18 will be the x
3, 6 .
coordinates of the points on
The solutions are sometimes called the zeros, or roots, of the equation. They represent
the curve at which y
0. Those
2
the x coordinates of the points where the graph of the equation y
x
3x
18 crosses
are the points at which the
the x axis. In this case, the graph crosses the x axis at ( 3, 0) and (6, 0).
graph intercepts the x axis.
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