Applications of Quadratic Functions name ______period ___

1. Suppose you are tossing an apple up to a friend on a third-story balcony. After t seconds, the height of the apple in feet is given by . 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?

a. time to reach your friend ______

b. height it was caught ______

2. Gretchen throws a ball straight up in the air. The quadratic function models the height in feet of the ball after x seconds. How long was the ball in the air? How long did it take the ball to reach the maximum height before falling? What was the maximum height?

Graph the information on the graph.

a. how long was ball in the air ______

b. time to reach maximum height ______

c. maximum height _____

3. Water is shot straight up out of a water soaker toy. The quadratic function models the height in feet of a water droplet after x seconds. How long is the water droplet in the air? What was the maximum height of the water droplet? How long did it take to reach this height?

Graph the information.

a. how long was water droplet in air ______

b. time to reach its highest point ______

c. highest point ______

4. A bicyclist is riding at a speed of 20 mi/h when she starts down a long hill which is 585 ft long. The distance d she travels in feet can be modeled by the function , where t is the time in seconds. To the nearest second, how long will it take her to reach the bottom? ______

5. Suppose you throw a ball straight up from the ground with a velocity of 80 ft/s. As the ball moves upward, gravity slows it. Eventually the ball begins to fall back to the ground. The height h of the ball after t seconds in the air is given by the quadratic function .

a. How high does the ball go?

b. for how many seconds is the ball in the air before it hits the ground?

6. A record label uses the following function to model the sales of a new release, ,

whereas the number of albums sold is a function of , time, t, in days. On which day were the most albums

sold? What is the maximum number of albums sold on that day?

a. which day were most albums sold______b. maximum number of albums sold on that day ______

7. If a tightrope walker falls, he will land on a safety net. His height h in feet after a fall can be modeled by

, where t is the time in seconds. How many seconds will the tightrope walker fall before landing on the safety net? ______

8. A bald eagle snatches a fish from a lake and flies to an altitude of 256 ft. The fish manages to squirm free

and falls back down into the lake. Its height h in feet can be modeled by , where t is the

time in seconds. How many seconds will the fish fall before hitting the water?

Seconds to hit the water ______

9. The quadratic function that approximates the height of a javelin throw is where t is

the time in seconds after it is thrown and h is the javelin’s height I feet. How long will it take for the javelin

to hit the ground?

Time to hit the ground ______

10. The barber’s profit p each week depends on his charge c per haircut. It is modeled by the equation

. What price should he charge for the largest profit? ______