Chapter 6 Quadratic Equations By Factoring Worksheet With Answer Key - Mcgraw-Hill Page 4
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HAPTER
OLYNOMIALS AND
OLYNOMIAL
UNCTIONS
C H E C K Y O U R S E L F 4
2
Solve 2x
10x
48
0.
In Chapter 3, we introduced the concept of a function and later expressed the equation
of a line in function form. Another type of function is called a quadratic function.
Definitions: Quadratic Function
A quadratic function is a function that can be written in the form
2
f(x)
ax
bx
c
in which a, b, and c are real numbers and a
0.
2
2
For example, f(x)
3x
2x
1 and g(x)
x
2 are quadratic functions. In working
with functions, we often want to find the values of x for which f(x)
0. As in quadratic
equations, these values are called the zeros of the function. They represent the x coordi-
nates of the points where the graph of the function crosses the x axis. To find the zeros of a
quadratic function, a quadratic equation must be solved.
Example 5
Finding the Zeros of a Function
2
Find the zeros of f(x)
x
x
2.
2
NOTE
The graph of
To find the zeros of f(x)
x
x
2, we must solve the quadratic equation f(x)
0.
2
f(x)
x
x
2
f(x)
0
intercepts the x axis at the
points (2, 0) and ( 1, 0), so 2
2
x
x
2
0
and
1 are the zeros of the
function.
(x
2)(x
1)
0
x
2
0
or
x
1
0
x
2
x
1
or
1, 2
The zeros of the function are
1 and 2.
C H E C K Y O U R S E L F 5
2
Find the zeros of f(x)
2x
x
3.
C H E C K Y O U R S E L F A N S W E R S
1
1. 4, 5
2. (a) 0,
8 ; (b) 4,
4
3.
, 2
4.
3, 8
3
3
1,
5.
2
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