Question 381887
Suppose you kick a football and it follows a trajectory. The height X will be modeled by a quadratic function because (well, I need calculus to explain why it's quadratic):

{{{V = int(a, dt) + v_0 = at + v_0}}}

{{{X = int(V, dt) + x_0 = int ((at + v_0), dt) = (1/2)at^2 + (v_0)t + x_0}}}

Hence, X is a quadratic function in terms of t. The vertex represents the time t where the maximum height is attained, and X(t) gives the maximum height (assuming air resistance is negligible).