A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h( t) = -16t2 + 96t + 14, where t is the time (in seconds) since the rocket was launched. What is the rocket’s maximum height and when does this occur.

s(2) = 38 meters

I don't know if you are a calculus student, but since calculus is the easiest way to solve this, that's what I used.  The position equation is

and the velocity function, the first derivative, is

From Physics, you should know that the velocity of an object is 0 at its highest point.  That means that if we sub in a 0 for the velocity and solve for t, we find the time at which the object is at its highest point.  That is:

and

By the Zero Product Property,

-12 definitely does not equal 0, so that means that

t - 2 = 0 and

t = 2 seconds.

So at 2 seconds, the object is at its highest point.  Go back to the position function now and sub in a 2 for t to find the height of the object at 2 seconds.

so

s(2) = 38 meters

the correct answer is 1.7