Question 1021026

I need help with this problem. Please help me and show all work. Thanks


A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+128t+144
h(t)=-16t^2+128t+144 models the ball's height about the ground, h(t)
 in feet, t seconds after it was thrown.

 a) What is the maximum height of the ball?

   _________feet


 b) How many seconds does it take until the ball hits the ground?

   _________ seconds
<pre>Maximum height occurs at {{{x = (- b)/(2a)}}}, or at {{{x = (- 128)/(2 * - 16)}}}, or at: {{{x = 4}}}
Maximum height at {{{x = 4}}} is: {{{y = - 16(4)^2 + 128(4) + 144}}}, or {{{y = - 256 + 512 + 144}}}, or maximum height reached = {{{highlight_green(matrix(1,2, 400, ft))}}} 

Ball hits the ground when y, or height = 0, so we get:
{{{0 = - 16t^2 + 128t + 144}}}
{{{- 16(0) = - 16(t^2 - 8t - 9)}}} ---- Factoring out GCF, - 16
{{{0 = t^2 - 8t - 9}}}  
0 = (t - 9)(t + 1)
0 = t - 9        OR          0 = t + 1
t, or time it takes ball to hit the ground = {{{highlight_green(matrix(1,2, 9, seconds))}}}            OR          - 1 = t (ignore)