Answer:
a) 64 feet
b)  3 seconds 
Step-by-step explanation:
a)
The maximum height of 
 can be bound by finding the y-coordinate of the vertex of 
.
Compare this equation to 
 to find the values of 
.


.
The x-coordinate of the vertex can be found by evaluating:



So the x-coordinate of the vertex is 1.
The y-coordinate can be found be evaluating 
 at 
:




So the maximum height of the rocket is 64 ft high.
b) 
When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.
So we are trying to find the second t such that:

I'm going to divide both sides by -16:

Now we need to find two numbers that multiply to be -3 and add to be -2.
Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

This implies we have either 
 or 
The first equation can be solved by adding 3 on both sides: 
.
The second equation can be solved by subtracting 1 on both sides: 
.
So when 
 seconds, is when the rocket has hit the ground.