The equation of the path followed by the ball is given by y = -4x^2 + 8x where x represents the horizontal coordinate and y is the corresponding height.

The graph of the path followed by the ball is:

The ball is at its highest point when the curvature of the graph changes. At this point the first derivative of the function f(x) = -4x^2 + 8x is equal to 0

f'(x) = -8x + 8

f'(x) = 0

=> -8x + 8 = 0

=> x = 1

At x = 1, f(x) = -4 + 8 = 4

**The ball is at the highest point when x = 1 and its height at this point is equal to 4.**