Scholarship Algebra II
Quadratic Word Problems
Solve each of the following word problems.
1. An army is trying to invade a foreign city with a huge wall around it. A cannon launches a cannonball in
an arc through the air modeled by the quadratic function ℎ = −16𝑡 2 + 80𝑡, where h is the height of
the cannonball (in ft) and t is the amount of time it was in the air (in sec).
a. What is the maximum height of the cannonball?
b. The wall surrounding the city is 85 ft. tall. Can the cannonball clear the wall?
2. A man catapults a watermelon off of a building. The path that the watermelon takes is modeled by the
quadratic ℎ = −8𝑠 2 + 24𝑠 + 46, where h is the height of the watermelon in feet and s is the number
of seconds that it has been in the air.
a. How high is the watermelon after 4 seconds?
b. How high does the watermelon get at its highest point? How long does it take to get there?
c. How high is the watermelon after 0 seconds? What does that number tell you?
3. A boy launches a bottle rocket into the air. The rocket follows a path modeled by the quadratic
h  36t  6t 2 , where h is the height of the rocket (in ft) of the rocket off the ground and t is the time (in
seconds) that the rocket has been in the air.
a. How high will the rocket be after 1 second?
b. How high will the rocket be at its highest point? How long will it take for it to get there?
c. How high was the rocket after 0 seconds? Why does that make sense?
4. The function 𝑅 = −3𝑝2 + 60𝑝 + 1060 models the daily revenue for a company that makes DVDs,
where R is the revenue and p is the price per DVD.
a. If the company charged $16 per DVD, how much would they make each day?
b. What is the maximum amount that they can make per day?
5. The height of a punted football can be modeled with the function ℎ = −0.01𝑥 2 + 1.18𝑥 + 2, where h
is the height of the ball (in ft) and x is the horizontal distance (in ft).
a. How high does the football get in the air?
b. The nearest defensive player is standing 5 ft away from the kicker. How high will he have to
reach to block the punt?
c. How high is the ball after it has travelled 0 yards horizontally? Why does that make sense?
(Think about a punted football!)
6. A company that makes car tires models its production costs with the quadratic equation 𝐶 =
0.000015𝑥 2 − 0.03𝑥 + 35, where C is the cost of making the tires and x is the number of tires
produced each day.
a. If the company makes 400 tires each day, how much will it cost them?
b. How many tires should the company make to minimize the cost of producing the tires? How
much will that cost?