Intermediate Algebra (11th edition)

Graph each parabola. ( Use the results of Exercises 5 – 8to help graph the parabolas in Exer-
cises 23 – 26.) Give the vertex, axis, domain, and range. See Examples 4, 8, and 9.

Solve each problem. See Examples 6 and 7.

33.Find the pair of numbers whose sum is 40 and whose product is a maximum. (Hint:Let
xand represent the two numbers.)

34.Find the pair of numbers whose sum is 60 and whose product is a maximum.

35.Polk Community College wants to construct a rectangular
parking lot on land bordered on one side by a highway. It has
280 ft of fencing that is to be used to fence off the other three
sides. What should be the dimensions of the lot if the enclosed
area is to be a maximum? What is the maximum area?

36.Bonnie Wolansky has 100 ft of fencing material to enclose a
rectangular exercise run for her dog. One side of the run will
border her house, so she will only need to fence three sides.
What dimensions will give the enclosure the maximum area? What is the maximum area?

37.If an object on Earth is projected upward with an initial
velocity of 32 ft per sec, then its height after tseconds is
given by

Find the maximum height attained by the object and the

number of seconds it takes to hit the ground.

38.A projectile on Earth is fired straight upward so that its
distance (in feet) above the ground tseconds after firing is
given by

Find the maximum height it reaches and the number of

seconds it takes to reach that height.

s 1 t 2 =- 16 t^2 + 400 t.

s 1 t 2 =- 16 t^2 + 32 t.

40 - x

x= 3 y^2 + 12 y+ 5 x= 4 y^2 + 16 y+ 11

x=-

1

2

x=- y^2 - 4 y- 6

1

5

y^2 + 2 y- 4

x= 1 y+ 222 + 1 x= 1 y+ 322 - 2

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

SECTION 9.6 More About Parabolas and Their Applications 549

0 x

y

(^0) x
y
0
x
y
0 x
y
0 x
y
(^0) x
y
x x
Concept Check Match each equation in Exercises 17 – 22 with its graph in choices A – F.

20.x=y^2 + 6 y+ 3 21.x=-y^2 - 2 y+ 4 22.x= 3 y^2 + 6 y+ 5

y=-

1

2

y= 2 x^2 + 4 x- 3 y=-x^2 + 3 x+ 5 x^2 - x+ 1

A. B. C.

D. E. F.