Find the vertex and the intercepts and then graph the

Find the vertex and the intercepts, and then graph the function g ( x ) = x
2
− 2 x − 2.
EXAMPLE 3
Find the vertex and the intercepts, and then graph the function f ( x ) = − 2 x
2
+ 4 x − 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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