Quadratic Formula Word Problems
1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function ht= -16t2+16t+480, where t is time in seconds and h is the height in feet.
a. How long did it take for Jason to reach his maximum height?
b. What was the highest point that Jason reached?
c. Jason hit the water after how many seconds?
2. If a toy rocket is launched vertically upward from the ground with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation ht=-16t2+128t (if air resistance is neglected).
a. How long will it take for the rocket to return to the ground?
b. After how many seconds will the rocket be 112 feet above the ground?
c. How long will it take the rocket to hit its maximum height?
d. What is the maximum height?
3. A manufacturer can model its profit P in thousands of dollars by P=-n2+32n+50, where n represents the number of items sold.
a) What is the profit (in dollars) made from 30 items sold?
b) What is the maximum profit that can be made by the company?
c) What is the profit made by selling 35 items? Explain the answer you calculate.
4. It is predicted that population p of mosquitos can be modeled by p=3t2+10t+2, where t is time in days. How many days would it take for the population to increase to 90?
5. The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
6. In a right triangle, the length of the longer leg is 7 inches more than the length of the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg. Find the length of all 3 sides.
7. The length of a rectangle is 4 less than twice the width. The area of the rectangle is 70. Find the dimensions of the rectangle.
8. A square is altered so that one dimension is increased by 4, while the other dimension is decreased by 2. The area of the resulting rectangle is 55. Find the area of the original square.