Algebra 2
Minimums and Maximums
Name____________________________________ Period___________
1. The Brick Oven Bakery sells more loaves of bread when it reduces its price, but then its profits
change. The function y
100(x 1.75)2 300 models the bakery’s profits, in dollars, where x is
the price of a loaf of bread in dollars.
a)
b)
c)
d)
What is the domain of this function?
Find the daily profit for selling the bread at $1.25 a loaf.
What price should the bakery charge to maximize its profit?
What is the maximum profit?
2. A skating rink manager finds that revenue R based on an hourly fee F for skating is represented by the
function R
480(F 3.25)2 5070 . What hourly fee will produce maximum revenue?
3. Suppose you are tossing an apple up to a friend on a third-story balcony. The height h of the apple in
feet is given by h 16(t 12)2 24 where t is time in seconds. Your friend catches the apple just as
it reaches its highest point. How long does the apple take to reach your friend, and at what height
above the ground does your friend catch it?
4. You kick a ball over a 5 ft. fence and it follows a parabolic path. The ball barely clears the fence and
lands 10 feet from the fence on the opposite side. Using the fence as the axis of symmetry, write an
equation that approximates the path of the ball (let the origin be the starting point of the ball).
5. The temperature of a patient during an illness is given by the function T
0.1d 2 1.2d 98.2 where
T is the patient’s temperature and d is the number of days after the onset of the illness.
a) On what day was the patient’s temperature the highest?
b) What was the patient’s highest temperature?
6. A software firm estimates that it will sell N units of a new CD-ROM game after spending A dollars on
advertising as modeled by the function N
A2 300A 6 where A is measured in thousands of
dollars.
a) For what advertising expenditure will the greatest number of games be sold?
b) How many games will be sold for that amount?
7. A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the
owners find that the profit p can be modeled by the function p
15t 2 600t 50 , where t
represents the ticket price in dollars.
a) What price gives the maximum profit?
b) What is the maximum profit?
8. The rabbit population on a small island is observed to be given by the function
p 0.4t 2 120t 1000 where t is the time in months since observations began.
a) When is the maximum population attained?
b) What is that maximum population?
c) When does the rabbit population disappear from the island? You may need to graph the
function on a calculator to find out.
Algebra 2
9. A farmer wants to construct a rectangular pen for his pigs using the side of his barn as one side of the
pen and 120 feet of fencing for the other 3 sides. In order to make the area inside the pen as large as
possible, what should be the dimensions of the pen?
10. In your subdivision you have an area planted with wildflowers and trails to walk. To keep the area
natural, you want to enclose the largest rectangular area possible with 2000 feet of fencing.
a) Write an equation for the area A.
b) Find the dimensions that will give the maximum area.
c) What is the maximum area?
16t 2 v 0t s 0 which represents the height s (in feet) of an object
For #'s 11-13, use the function s
projected vertically upward with an initial velocity v0 (in ft/sec) from an initial height s0 (in feet).
11. The tallest structure in the United States, at 2063 feet, is the KTHI-TV tower in North Dakota. How
long would it take an object falling freely from the top of the tower to reach the ground?
12. An object is propelled vertically upward from the ground with an initial velocity of 60 ft/sec.
a) How high will the object be in 2 seconds?
b) When does the object reach its highest point?
c) How high is the object at this highest point?
d) Referring back to part a, at 2 seconds was the object on its way up or on its way down?
13. A ball is thrown vertically upward from the top of a building 96 feet tall with an initial upward
velocity of 80 ft/sec.
a) After how many seconds does the ball reach its highest point?
b) How high off the ground is the ball at its peak?
c) After how many seconds does the ball hit the ground? Hint: use a graphing calculator.