Question

A pomegranate is thrown from ground level straight up into the air at time t=0 with velocity 128 feet per second. Its height in feet at t seconds is f(t)=16t^2+128t. Find the time its hits the ground and the time it reaches its highest point.

Answer 1

Your equation should be
f(t) = - 16t^2 + 128t

so
-16t^2 + 128t = 0
t^2 - 8t = 0
t(t-8) = 0
t = 0 ----> when you tossed it
t = 8 ----> when it lands

so it reached the hightest point at the midpoint of that 8 seconds, namely at 4 seconds
f(4) = -16(4^2) + 128(4)
= 256 ft

Wow!, That is quite a feat to through a pomegranate 256 feet into the air!!!!!