Function

a)  Max will be at the VERTEX of the parabola. the max value can be quickly found by t= -b/2a

      -96/-32 = t = 3

      sub 3 into the equation to find h-max     = 644

b. found in answer a to be t=3 sec

c 0 = -16t^2+96t+500     use quadratic fomual to find t=9.34 sec to the ground

d. 300 = 16t^2+96t+500                                               t=7.63

Here is a graph: