Question

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A catapult launches a boulder with an upward velocity of 184 feet per second. The height of the boulder, h, in feet after t seconds is given by the function h(t)=-16t^2+184t+20. What is the boulder's maximum height? How long does it take the boulder to reach its maximum height? Round to the nearest hundredth if necessary.

A. Reaches a maximum height of 11.6 feet after 5.75 seconds.
B. Reaches a maximum height of 549 feet after 11.5 seconds.
C. Reaches a maximum height of 549 feet after 5.75 seconds.
D. Reaches a maximum height of 23.2 feet after 11.6.

Answer 1

I can see to ways to find the maximum height. First way, is to complete the square and change the function into vertex form or by differentiation. Do you know how to do differentiation?

Answer 2

No :(

Answer 3

kk, what about completeing the square?

Answer 4

Do you know how to change the function into vertex form?

Answer 5

I know about it, but don't really understand :/

Answer 6

the vertex is the highest point on your parabola function

Answer 7

Ohhh ok

Answer 8

and so you want to find the coordinates of the vertex