Flights of leaping animals typically have parabolic paths. The figure illustrates a frog jump superimposed on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet. Find a standard equation for the path of the frog. Assume a = 1.

Answer 1

Since the leap travels 9 feet, the function has zeros at x=0,9, so

y(x) = ax(x-9)

When x = 9/2,
y(9/2) = a(9/2)(-9/2) = -81/4 a

Why should we assume a=1?

If -81/4 a = 3a we are in trouble.

I think there's something wrong with the way the problem is stated. Either that, or (missing a diagram) my assumption that the height is zero at x=0,9 is wrong.