The initial height is 80 feet above ground and the initial speed is 64 ft/s. Since my units are "feet", then the number for gravity will be 16, and my equation is:

s(t) = -16t2 + 64t + 80

They want me to find the maximum height. For a negative quadratic like this, the maximum will be at the vertex of the upside-down parabola. So they really want me to find the vertex. From graphing, I know how to find the vertex; in this case, the vertex is at (2, 144):

h = -b/2a = -(64)/2(-16) = -64/-32 = 2

k = s(2) = -16(2)2 + 64(2) + 80 = -16(4) + 128 + 80 = 208 - 64 = 144

But what does this vertex tell me? According to my equation, I'm plugging in time values and extracting height values, so the input "2" must be the time and the output "144" must be the height.   Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved

It takes two seconds to reach the maximum height of 144 feet.