h = - 16t^2 + 80t The best way to solve for t is to complete the square. h = -16(t^2 - 5t) h= - 16(t^2 - 5t + (5/2)^2) - (-16 * 25/4) h= -16(t^2 - 5t + (5/2)^2 )^2 + 100 h = -16(t^2 - 5/2)^2 + 100
Here's what all that tells you. 1. It reached a maximum height of 100 feet. 2. It reaches a maximum height (the sign in front of the 16 is minus). That means that the quadratic is a minus. 3. The time needed to reach this maximum height is 5/2 seconds or 2.5 seconds. 4. Here's the biggy. The time it was in the air was 2 times as much as 2.5 second. The reason is that the ball has to come down again.
Summary Max height = 100 feet. <<<< answer Time in the air = 5 seconds <<<< answer
Just to confirm what I said, a graph is included. You should see the following things. The graph cuts the x axis at 5 The graph has a maximum of (2.5,100) The graph also cuts the x axis at 0. This was the starting time of the ascent. It's always a good idea to get a graph from Desmos if you can.