A security fence encloses a rectangular area

1. A college is creating a new rectangular parking lot. The length is 0.08 mile longer than the width and the area of the parking lot is 0.024 square mile. Find the length and width of the parking lot. Show your work.

The width is ____?

The length is ___?

2. Greg drove at a constant speed in a rainstorm for 222 miles. He took a break, and the rain stopped. He then drove 126 miles at a speed that was 5 miles per hour faster than his previous speed. If he drove for 9 hours, find the car’s speed at each part of the trip? Show your work.

The rate of the car in the rain was _____?

The rate of the car in no rain was _____?

3. The number of inmates N (measured in thousands) in federal and state prisons can be approximated by the equation N= -2.02x^2 + 77.81x + 749, where x is the number of years since 1990. In what year was the number of inmates expected to be 1,194,690? Show your work.

The number of inmate was expected to be 1,194,690 in the year _____?

4. Bob drove from home to work at 80 mph. After work the traffic was heavier, and he drove home at 25 mph. His driving time to and from work was 1 hour and 3 minutes. How far does he live from his job? Show your work.

Bob lives ____ miles from his job.

5. Sales for SUVs (sports utility vehicles) in the United States (in millions) for the years 1990-1999 can be modeled by the quadratic function shown below. Show your work.

F(x)=0.016x^2 + 0.124x + 0.787

Here, x=0 represents 1990, x=1 represents 1991, and so on. Use the model to approximate sales in 1998.

Sales in 1998 were approximately _____ million SUVs. (round to the nearest tenth as needed)

6. A security fence encloses a rectangular area on one side of a park in a city. Three sides of fencing are used, since the fourth side of the area is formed by a building. The enclosed area measures 2592 square feet. Exactly 144 feet of fencing is used to fence in three sides of this rectangle. What are the possible dimensions that could have been used to construct this area? Show your work.

The shorter dimension of the fenced area is ____ feet.

The longer dimension of the fenced area is ____ feet.

7. Find the coordinates of the vertex and the intercepts of the following quadratic function. When​necessary, approximate the​ x-intercepts to the nearest tenth. Show your work.

f(x)=x2−8x−9

The vertex is ____?

The intercepts are ____?

8. Find the coordinates of the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist) of the following quadratic function. Show your work.

​g(x)=−x2−8x+9

The vertex of the quadratic function g(x) is ___? (Type an ordered pair)

X intercept is _____? (if any exist)

Y intercept is _____? (if any exist)

9. Find the coordinates of the vertex and the intercepts of the following quadratic function. When​ necessary, approximate the​ x-intercepts to the nearest tenth. Show your work.

​p(x)=2x2+8x+2

The vertex is_____?

Coordinates of the intercepts are ______?

10. Find the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist).

f(x)=x2−10x+25

The vertex is _____? (Ordered pair)

Y-intercept is _____?

X-intercept is _____?

11. Find the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist).

p(x)=x2−6x+8

The vertex is _____? (Ordered pair)

Y-intercept is _____?

X-intercept is _____?

12. Find the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist), and then graph the function.

p(x)=2x2+4x−12

The vertex is _____? (Ordered pair)

Y-intercept is _____?

X-intercept is _____?

13. Find the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist), and then graph the function.

p(x)=−x2+12x−20

The vertex is _____? (Ordered pair)

Y-intercept is _____?

X-intercept is _____?

14. Find the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist), and then graph the function.

r(x)=3x2+6x+4

The vertex is _____? (Ordered pair)

Y-intercept is _____?

X-intercept is _____?

15. Find the​ vertex, the​ y-intercept, and the​ x-intercepts (if any​ exist), and then graph the function.

f(x)4x2−4

The vertex is _____? (Ordered pair)

Y-intercept is _____?

X-intercept is _____?

16. Determine, without​ graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.

f(x)=−2x2+16x−5

Does the quadratic function f have a minimum value or a maximum value?

What is the value?

17. ​Determine, without​ graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.

18. f(x)=3x2+24x−6

Does the quadratic function f have a minimum value or a maximum value?

What is the value?

19. ​Determine, without​ graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.

f(x)=2x2+20x−8

Does the quadratic function f have a minimum value or a maximum value?

What is the value?

20. Suppose that the manufacturer of a DVD player has found​ that, when the unit price is p​ dollars, the revenue R​ (in dollars) as a function of the price p is R(p)=−2.5p2+500p.

(a) For what price will the revenue be​ maximized?

(b) What is the maximum​ revenue?

21. The daily profit P in dollars of a company making tables is described by the function

P(x)=−5x2+240x−2560​, where x is the number of tables that are manufactured in 1 day. Use this information to find P(29​).

P(29) = _____? (simplify your answer)

22. The daily profit P in dollars of a company making tables is described by the function

P(x)=−5x2+280x−3675​, where x is the number of tables that are manufactured in 1 day. The maximum profit of the company occurs at the vertex of the parabola. How many tables should be made per day in order to obtain the maximum profit for the​ company? What is the maximum​ profit?

23. Susan throws a softball upward into the air at a speed of 32 feet per second from a

104 platform. The distance upward that the ball travels is given by the function d(t)=−16t2+32t+104. What is the maximum height of the​ softball? How many seconds does it take to reach the ground after first being thrown​ upward? ​ (Round your answer to the nearest​ tenth.)

24. A security fence encloses a rectangular area on one side of a park in a city. Three sides of fencing are​ used, since the fourth side of the area is formed by a building. The enclosed area measures 968 square feet. Exactly 88 feet of fencing is used to fence in three sides of this rectangle. What are the possible dimensions that could have been used to construct this​ area?

25. Palo Alto College is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 400 feet of fencing to fence off the other three sides. What dimensions should the lot have if the enclosed area is to be a​ maximum?

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