Tyrone launches a toy rocket into the air with an initial upward velocity of 49 ft/s and an initial height of 0 ft.

a. How long will it take the rocket to reach its maximum height? Round to the nearest hundredth.
b. How high above the ground will it be? Round to the nearest tenth.
c. What is the range of the function?
d. Why is there a maximum point on the graph of this function?

Answers:
A. 1.53 s; 37.5 ft; 0 ≤ h ≤ 37.5; the rocket will continue to travel upwards until gravity pulls it back to Earth, so there is a maximum point on the graph which opens downward.
B. 4.50 s; –103.5 ft; −103.5 ≤ h ≤ 0; the rocket will continue to travel upwards until gravity pulls it back to Earth, so there is a minimum point on the graph which opens upward.
C. 1.53 s; 49 ft; 0 ≤ h ≤ 49; the rocket will continue to travel upwards until gravity pulls it back to Earth, so there is a maximum point on the graph which opens downward.
D. 3.06 s; 1.1 ft; 0 ≤ h ≤ 1.1; the rocket will continue to travel upwards until gravity pulls it back to Earth, so there is a maximum point on the graph which opens downward.