Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t)=-16t[square] + 16t + 480, where t is the time in seconds and h is the height in feet. How long did it take for Jason to reach his maximum height? What was the highest point that Jason reached? Jason hit the water after how many seconds?

Solution:

h(t)=-16t^2+16t+480 = -16(t^2-t-30)=-16((t-0.5)^2-30.25)=-16(t-0.5)^2+484

When t=0.5, h is max, h=484

It takes 0.5 seconds to reach his maximum height, highest is 484 m

h(t)=0 --> t=6

So Jason hit the water after 6 seconds