Let's imagine this function in real life. We the rocket is launched, it will follow a path similar to a negative parabola (a 'frown', as the coefficient of x^2 is negative).
So, we can work out the answer by finding the vertex of this of this 'graph', as this represents the highest point that the rocket will reach during its journey. To find t, we use the expression -b/2a (these letters are from the format of the quadratic equation ax^2+bx+c, so in this case a= -16 and b= 96):
-b/2a
-(96)/2(-16)
-96/-32
t=3
Now, we can plug 3 back into the function:
h(t)= -16t^2+96t
h(3)= -16(3^2)+96(3)
h(3)= -16(9)+96(3)
h(3)= -144+288
h(3)= 144
Therefore, the maximum height attained by the rocket is 144ft, at t = 3 seconds.
