Question 314607
I think that the max height is 69 feet, and it occurs at 2 seconds.


Make sure you complete the square:


h(t) = -16t^2+64t+5
= -16(t^2 - 4t) + 5
=-16(t^2 -4t + 4) + 5 + 64
=-16(t-2)^2 + 69


This a parabola with vertex at (2,69). 


If you want to find the time that it takes to hit the ground, set h=0 and use the quadratic formula to solve for t.

0=-16t^2+64t+5


The quadratic formula should give you two answers: t=-0.77 and t=4.077


You have to choose the positive answer, as time cannot be negative.


Therefore, the ball hits the ground at 4.077 seconds.