Intermediate Algebra (11th edition)

548 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

y

x

a > 0

These graphs

represent functions.

y

x

(h, k) a < 0

(h, k)

00

Graphs of Parabolas

Equation Graph

or

or

xa 1 yk 22 h

xay 2 byc

ya 1 xh 22 k

yax^2 bxc

y

x

y

(^00) x
a > 0
(h, k)
a < 0
(h, k)
These graphs are not
graphs of functions.
Complete solution available
on the Video Resources on DVD
Concept Check In Exercises 1– 4, answer each question.
1.How can you determine just by looking at the equation of a parabola whether it has a ver-
tical or a horizontal axis?
2.Why can’t the graph of a quadratic function be a parabola with a horizontal axis?
3.How can you determine the number of x-intercepts of the graph of a quadratic function
without graphing the function?
4.If the vertex of the graph of a quadratic function is , and the graph opens down,
how many x-intercepts does the graph have?
Find the vertex of each parabola. See Examples 1– 3.

Find the vertex of each parabola. For each equation, decide whether the graph opens up,

down, to the left, or to the right, and whether it is wider, narrower, or the same shape as the

graph of. If it is a parabola with vertical axis, find the discriminant and use it to de-

termine the number of x-intercepts. See Examples 1–3, 5, 8, and 9.

13. 14.

15. 16.x=

1

2

x= y^2 + 10 y- 5

1

3

y^2 + 6 y+ 24

ƒ 1 x 2 =-x^2 + 5 x+ 3 ƒ 1 x 2 =-x^2 + 7 x+ 2

ƒ 1 x 2 = 2 x^2 + 4 x+ 5 ƒ 1 x 2 = 3 x^2 - 6 x+ 4

y=x^2

ƒ 1 x 2 =x^2 +x- 7 ƒ 1 x 2 =x^2 - x+ 5

ƒ 1 x 2 =- 2 x^2 + 4 x- 5 ƒ 1 x 2 =- 3 x^2 + 12 x- 8

ƒ 1 x 2 =x^2 + 8 x+ 10 ƒ 1 x 2 =x^2 + 10 x+ 23

1 1, - 32

In summary, the graphs of parabolas fall into the following categories.

9.6 EXERCISES