### Home > PC > Chapter 8 > Lesson 8.2.1 > Problem8-77

8-77.

If a ball is thrown vertically upward with a velocity of $32$ ft/s, its height after t seconds is given by the equation $s(t)=32t-16t^2$. At what instant will the ball be at its highest point, and how high will it rise?

1. Set the function $=0$.

2. Factor.

3. Solve for the $t$-intercepts.

4. Take the average of the $x$-intercepts to locate the $t$-coordinate of the vertex.

5. Substitute that $t$-value into the original equation to calculate the maximum height.