A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function h(x)= -1/225x^2+ 2/3x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet. On the set of
axes below, graph the function y = h(x) over the interval
0 = X = 150. (Use the graph to show this)

Determine the vertex of y = h(x). Interpret the meaning of this vertex in the context of the problem.

The goal is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the the goal post? Justify your answer.