Find the vertex and the intercepts, and then graph the function g(x) = x2−2x−
2.
EXAMPLE 3Find the vertex and the intercepts, and then graph the function f(x) = −2x2+ 4x−
3.
.
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The
y
-intercept is (0, -3).
If there are any
x
-intercepts, they will occur when
f(x)
= 0. We use the quadratic formula to solve
−
2
x
2
+ 4
x
−
3 = 0 for
x
.
Because
yields an imaginary number, there are no real roots. Thus, there are no
x
-intercepts for the graph of the function. That is, the graph does not intersect the
x
-axis.
We know that the parabola opens
downward
. Thus, the vertex is a maximum value at (1,
−
1). Since this graph has no
x
-intercepts, we will look for three additional points to help us in drawing the graph. We try
f
(2),
f
(3), and
f
(
−
1).
Student Practice 3
Find the vertex and the intercepts, and then graph the function
g
(
x
) =
−
2
x
2
−
8
x
−
6.
583584
9.5 Exercises
Find the coordinates of the vertex, the y
−
intercept, and the x
−
intercepts (if any exist) of each of the following quadratic functions. When necessary, approximate the x
−
intercepts to the nearest tenth.
1.
f
(
x
) =
x
2
−
2
x
−
8
2.
f(x) = x
2
−
4x
−
5
3.
g
(
x
) =
−
x
2
−
8
x
+ 9
4.
g(x)
=
−
x
2
+ 4
x
+ 21
5.
p
(
x
) = 3
x
2
+ 12
x
+ 3
6.
p(x)
= 2
x
2
+ 4
x
+ 1
7.
r
(
x
) =
−
3
x
2
−
2
x
−
6
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8.
f(x)
=
−
2
x
2
+ 3
x
−
2
9.
f
(
x
) = 2
x
2
+ 2
x
−
4
10.
f
(
x
) = 5
x
2
+ 2
x
−
3
In each of the following exercises, find the vertex, the y
−
intercept, and the x
−
intercepts (if any exist), and then graph the function.
11.
f(x)
=
x
2
−
6
x
+ 8
12.
f
(
x
) =
x
2
+ 6
x
+8
13.
g
(
x
) =
x
2
+ 2
x
−
8
14.
g
(
x
) =
x
2
−
2
x
−
8
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584585
15.
p
(
x
) =
−
x
2
+ 8
x
−
12
16.
p
(
x
) =
−
x
2
−
8
x
−
12
17.
r
(
x
) = 3
x
2
+ 6
x
+ 4
18.
r
(
x
) =
−
3
x
2
+6
x
−
4
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