Question

H(t)=−16t2+28t (first 2 is an exponet)

The function h(t) gives the approximate height, in feet, of a dolphin's jump out of water, where t represents the time, in seconds. What is the total length of time, in seconds, it took the dolphin to complete one jump? Show your work.

Answer 1

It takes 1.75 seconds.

We want to know when the dolphin hits the water again. We set h(t) = 0 to do this:
0 = -16t² + 28t

We will factor out the GCF:
0 = 4t(-4t+7)

Using the zero product property, we know that either 4t=0 or -4t+7=0:

4t=0
Divide both sides by 4:
4t/4 = 0/4
t = 0

This is when the dolphin first jumps.

-4t+7=0

Subract 7 from both sides:
-4t = -7

Divide both sides by -4:
-4t/-4 = -7/-4
t = 7/4 = 1.75