Question

On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t^2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is _______ feet

Answer 1

The maximum height is 144 feet.

The maximum height is the y-coordinate of the vertex.  To find the vertex, we first use x = -b/2a.  For our information, that is x=-64/2(-16) = -64/-32 = 2.

Now we substitute this into the equation:
y = -16(2²) + 64(2) + 80 = -64 + 128 + 80 = 144