Question

A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -2x 2 + 8x. At what point does the ball hit the ground?

Answer 1

Check the picture below.  That's about what a parabola for an "initial velocity" case would look like.

anyhow, it hits the ground at two points, when it began, and when it came back down, and that happens when y = 0.

$\bf h(x)=-2x^2+8x\implies \stackrel{h(x)}{0}=-2x^2+8x\implies 0=-2x(x-4)\\\\ -------------------------------\\\\ 0=-2x\implies 0=x\qquad \impliedby \textit{when it began}\\\\ -------------------------------\\\\ 0=x-4\implies \boxed{4=x}\qquad \impliedby \textit{when it came back down}$