Question

"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?

The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"

Answer 1

2.25 seconds

88 feet high

Explanation:

For both questions, you're looking for the vertex of the parabolic curve this function models: a = -16 b = 72 c = 7

1. t-coordinate of vertex: t = -b/(2a) = -72/-32 = 2.25

2. h-coordinate of vertex: h(2.25) = -16(2.25)² + 72(2.25) + 7 = 88