CPM Homework Help : PC3 Problem 3-58

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?

Steps:

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.