QUADRATIC APPLICATIONS
Name: ________________________________ Block: _______
1. The difference of two numbers is 48. Find the minimum product of the two numbers.
2. Find two numbers whose sum is 36 and whose product is a maximum.
3. Find two numbers whose difference is 25 and whose product is a minimum.
4. The sum of x and y is -16. Find x and y so that xy is a maximum.
5. A rectangle has a perimeter of 40 meters. Find the dimensions of the rectangle with the maximum area.
6. Melissa plans to put a fence around her rectangular garden. She has 150 feet of fencing material to make the fence.
If there is to be a 10 foot opening left for an entrance on one side of the garden, what dimensions should the garden be
for maximum area?
7. Marc has 120 feet of fence to make a rectangular kennel for his dogs. If the house is to be used as one side of the
kennel, what would be the length and width for maximum area.
8. Morgan needs to paint a landscape for art class. She has 6 feet of framing material to frame the finished painting.
What should the dimensions of her canvas be for the painting to be of maximum area?
9. The circulation of the Charlotte Arts Council Newsletter is 50,000. Due to increased production costs, the council
must increase the current price of 40 cents per copy. According to a recent survey, the circulation of the newsletter will
decrease 5000 for each 10 cent increase in price. What price per copy will maximize the Arts Council’s income from the
newsletter?
10. A tour bus carries tourists through the historic district of Savannah, GA, serving 300 customers a day. The charge is
$8 per person. The owner estimates that the company would lose 20 passengers a day for every $1 increase in the fare.
What charge would be the most profitable for the tour bus company?
11. The Hoosier Commuter Airline transports about 800 passengers a week between Chicago and Fort Wayne. A round
trip ticket is $300. The company executives estimate that for each $5 increase in the ticket price, 10 passengers will be
lost to the competition. What ticket price would maximize income for the company?
12. Quick Cab runs a taxi service between the airport and business district. The charge for one-way service is $11.50.
The owners estimate the 30 passengers will be lost each day for each $1.50 increase in fare. If they currently service 320
passengers per day, what fare should they charge for maximum income?
13. Zach and Amy cut a 32-inch piece of wire into two pieces. Amy bent one piece into a square and Zach bent the
other into a rectangle that is 2 inches longer than it is wide. How long should they have cut each piece so that the sum
of the areas of the square and the rectangle are minimized?
14. The population of the United States from 1800 to 1890 can be approximated by the model:
POPULATION = 0.6942t2 + 6.183
where the population is given in millions of people and the time (t) represents the calendar year with t = 0
corresponding to 1800. If this model had continued to be valid up through present time, when would the population of
the US have reached 250 million?
15. The CN Tower in Toronto, Ontario is 1820 feet tall. An object is dropped from the tower. How long with it take for it
to hit the ground?
16. A bomber flying at 32,000 feet over level terrain drops a 500-lb bomb. How long will it take for the bomb to strike
the ground?
17. A one-story building is 14 ft longer than it is wide. It has 1632 square feet of floor space. Find the dimensions of the
building.
18. An object is fired upwards from the top of a 200 ft tower at a velocity of 80 ft/sec. The height of the object t seconds
after firing is given by the formula h(t) = -16t2 + 80t + 200. Find the maximum height reached by the object and the time
that it takes for that height to be reached.
19. A ball is thrown straight up with an initial velocity of 64 ft/sec. The height of the ball t seconds after it is thrown is
given by the formula h(t) = 64t – 16t2. What is the height of the ball after 1.5 seconds? What is its maximum height?
After how many seconds will it return to the ground?
20. The Empire State Building is 1250 feet high. If an object is thrown upwards from the top of the building at an initial
velocity of 35 feet per second, it’s height t seconds after it is thrown is given by the function h(t) = -16t2 + 35t + 1250.
How long will it be before the object hits the ground?