Algebra 2 Help on Graphs and X-Intercepts?

Question

Here's the problem I was given:
The height h(in feet) of an object thrown vertically upward (after t seconds), is given by the function h=-16t^2+vt+s (where v is the initial velocity in ft/sec, s is the initial height in ft.)

A ball is thrown upward with an initial velocity of 112ft/sec from an initial height of 128 ft, and allowed to fall on the ground. 
A) What is the maximum height it reached? 
B) At what time did it hit the ground? 

____ft,_____sec

I have one answer so far which is 8 seconds but I'm not sure if it's correct. If someone could solve it and answer with answers and the process of doing it, I would be extremely grateful.

Answer 1

When the ball is thrown upward, it goes in parabolic path.

The function of height is .

At, initial velocity and initial height 128ft.

.

A)

we can get the maximum height by changing this standard parabolic path into vertex form.

it is in the form , so here vertex .

So, the maximum height that the ball reached is 324ft.

 

B) The time taken to ball to hit the ground is

At the time of ball hitting the ground, the height of the ball is zero.

                 (The time is not negative)

It reaches the ground after 8 sec.