Answer
a) 0 seconds: 576 feet, 2 seconds: 672 feet, 4 seconds: 740 feet, 6 seconds: 480 feet
b) Eventually, $abs(-16t^2+80t) > 576$, so the function will have negative values.
c) $-16(t-9)(t+4)$
Work Step by Step
a)
$h(t)=-16t^2+80t+576$
$y=h(t)$
$t=0$
$y=-16t^2+80t+576$
$y=-16*0^2+80*0+576$
$y=-16*0+0+576$
$y=0+576$
$y=576$
$t=2$
$y=-16t^2+80t+576$
$y=-16*2^2+80*2+576$
$y=-16*4+160+576$
$y=-64+736$
$y=672$
$t=4$
$y=-16t^2+80t+576$
$y=-16*4^2+80*4+576$
$y=-16*16+320+576$
$y=-256+896$
$y=740$
$t=6$
$y=-16t^2+80t+576$
$y=-16*6^2+80*6+576$
$y=-16*36+480+576$
$y=-576+480+576$
$y=480$
c)
$-16t^2+80t+576$
$-16(t^2-5t-36)$
$-16(t-9)(t+4)$
