29Max height, projectile motion

A ball's height in feet after $\displaystyle t$ seconds is $\displaystyle h = -16t^2 + 64t + 80$. Find its maximum height and the time it hits the ground.

The ball peaks at 144 feet, reached at t = 2 s (the vertex of the downward parabola), and lands at t = 5 s, where h = 0. Vertex time: t = −64/(2·−16) = 2, giving h = 144. Ground time from factoring −16(t−5)(t+1)=0, keeping the positive root.