Question

Eva is jumping on a trampoline. Her height h at time t can be modeled by the equation h=-16t^2+20t+6. Would Eva reach a height of 14 feet?

Answer 1

Given the equation modeling Eva's height at time,t. To evaluate if she will reach height of 14 ft, we evaluate maximum height that she will reach.
At maximum height h'(t)=0
but
h(t)=-16t^2+20t+6
h'(t)=-32t+20=0
solving for t we get:
-32t=-20
t=20/32
t=5/8
thus the maximum height reached was:
h(5/8)=-16(5/8)^2+20(5/8)+6
h(5/8)=12.25 ft
Thus we conclude that she won't reach the height of 14 ft because her maximum height was 12.25 ft