23Max height of a parabola

A ball's height, in meters, $\displaystyle t$ seconds after it is thrown is $\displaystyle h(t) = -4.9t^2 + 19.6t + 2$. What is the ball's maximum height, in meters?

The ball's maximum height is 21.6 meters, reached at t = 2 seconds. Using t = −b/2a with a = −4.9, b = 19.6 gives t = 2, and h(2) = −19.6 + 39.2 + 2 = 21.6. Checking at t = 1.9 gives 21.591, slightly lower, confirming 21.6 is the peak.