Question 1154647
A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+80t+96
models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
 What is the maximum height of the ball?
How many seconds does it take until the ball hits the ground?
<pre>You don't have to do what the other person did. It's TOTALLY UNNECESSARY!
{{{matrix(1,3, h(t), "=", - 16t^2 + 80t + 96)}}}
Maximum height occurs at: {{{matrix(4,3, t, "=", (- b)/(2a), t, "=", (- 80)/(2 * - 16), t, "=", (- 80)/(- 32), t, "=", 2.5)}}}
With t = 2.5, maximum height of ball, or: {{{highlight_green(matrix(1,7, h(2.5), "=", - 16(2.5)^2 + 80(2.5) + 96, "=", - 100 + 200 + 96, "=", highlight(matrix(1,2, 196, feet))))}}} 
To find the time it takes for the ball to hit the ground, we set h(t) = 0. We then get: {{{matrix(3,3, 0, "=", - 16t^2 + 80t + 96,
- 16(0), "=", - 16(t^2 - 5t - 6),
0, "=", t^2 - 5t - 6)}}}
0 = (t - 6)(t + 1)
0 = t - 6                OR                 0 = t + 1
Time it takes to hit the ground, or: {{{highlight_green(matrix(1,4, t, "=", 6, seconds))}}}        OR            t = - 1 (ignore)
In other words, you don't have to COMPLETE the SQUARE, and you certainly DON'T have to use the quadratic equation formula! Unless you want to!!