The function that models the path of the football is:
h(x) = -1/225x^2 + 2/3x
In this function, x represents the horizontal distance that the football travels, and h(x) represents the height of the football above the ground at that distance.
The first term, -1/225x^2, represents the effect of gravity on the height of the football. As the football travels farther horizontally, it starts to fall back towards the ground due to the force of gravity. The coefficient -1/225 represents the rate at which the height of the football decreases due to gravity.
The second term, 2/3x, represents the initial height and the effect of the initial velocity of the football. This term gives the football an initial upward velocity that helps it clear the goal post. The coefficient 2/3 represents the initial velocity of the football.
Together, these two terms give the height of the football at any horizontal distance x.