4. A rock is thrown with a height equation of h = - 16t2 + 64t + 5 (where h is the height of the rock in feet at any given time of t in seconds). Will it reach a height of 50 feet? Explain your answer.

Yes, see below.

Step-by-step explanation:

Convert the equation to vertex form to find the maximum height:

h = - 16t2 + 64t + 5

= - 16 (t^2 - 4t) + 5

= - 16 [ (t - 2) ^2 - 4] + 5

= - 16 (t - 2) ^2 + 64 + 6

= - 16 (t - 2) ^2 + 69.

So the maximum height the rock reaches is 69 feet.

This height is reached at 2 time seconds.