A toy rocket is launched straight up

Question

A toy rocket is launched straight up from the roof of a garage with an initial velocity of 104 feet per second. The height  of the rocket in feet, at  seconds after it was launched, is described by h(t)=-16t^2+104t+18 .

Find the maximum height of the rocket. 

Answer 1

v(t) = h'(t) = - 32t + 104 = 0; t = 104/32 = 3.25 s

max h = h(3.25) = - 16·3.25² + 104·3.25 + 18 = 187 ft

Answer 2

The graph is a downward parabola with a peak at its apex. The maximum height is the y value at the apex.

The apex for the equation ax² + bx + c = y occurs at x = -b/2a

You can find the time to the peak (apex), then plug that into the h(t) equation to find h_max.

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