Question

A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by h(t)=-16t^2 +64t+336

Answer 1

The maximum height of the rocket booster is 368 feet.

The height of the rocket booster can be found by evaluating the given equation h(t) = -16
`t^2` + 64t + 336.

To find the maximum height, we need to determine the vertex of the quadratic function. The vertex can be found using the formula t = -b/2a, where a = -16 and b = 64.

Plug in the values of a and b into the formula to get:

t = -64/(2*-16)

= 2.

Substitute the value of t into the equation h(t) to find the maximum height:

h(2) =
`-16(2)^2` + 64(2) + 336

= 368 feet.