Module 2 29

Applications of Quadratic Functions

1. Laura owns and operates Aunt Linda’s Pecan Pies. She has learned that

her profits, P(x), from the sale of x cases of pies, are given by P(x) = 150x – x2.

a. The company will “break-even” when the profit is zero. How many cases of pies

should Laura sell in order to break-even? (Solve for x when P(x) = 0.)

b. How many cases of pies should she sell in order to maximize profit?

c. What is the maximum profit?

2. John wants to build a corral next to his barn. He has 300 feet of fencing to enclose

three sides of his rectangular yard.

a. What is the largest area that can be enclosed?

b. What dimensions will result in the largest yard?

3. The function V(t) = –3t2 + 140t + 824 models the number (in thousands), V(t), of

murders committed in a certain state in the United States t years after 1960.

Let t = 0 represent 1960, t = 1 represent 1961, and so on.

a. Determine the year in which the most violent crimes were committed.

b. Approximately how many violent crimes were committed during this year?

c. Using a graphing calculator, graph V(t). Were the number of violent crimes

increasing or decreasing during the years 2000 to 2005?

4. A ball is thrown vertically upward from the top of a building 1600 feet tall with an initial

velocity of 80 feet per second. The distance d(t), in feet, of the ball from the ground

after t seconds is

d(t) = 1600 + 80t – 16t2.

a. After how many seconds is the ball at its maximum height?

b. Find the maximum height of the ball.