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