Using the graph at the left, it shows the height in feet of a small rocket seconds after it is launched. The path of the rocket is given by the equation:

Question

h(t)=-16t^2+128t
What is the maximum height of the rocket?
(click on the graph)

Answer 1

The maximum height of the rocket can be found by determining the vertex of the parabolic trajectory, which occurs at the maximum point.
The formula for the vertex of a parabola given in the form y = ax^2 + bx + c is given by:
x = -b/(2a)

In this case, a = -16, b = 128,
x = -128/(2*(-16)) = 4

Now, we substitute x = 4 back into the given equation to find the maximum height h(4):
h(4) = -16(4)^2 + 128(4) = -256 + 512 = 256

Therefore, the maximum height of the rocket is 256 feet.