Question 938490
Since 's' predicts the height from the equation:
s=-2.7t^2+30t+6.5
Just by looking at the above equation we determine that it is a 
parabola (quadratic) (polynomial of degree 2)
that opens downwards (negative leading coefficient)
.
Therefore, the vertex will be the peak of its travel.
time t to arrive at peak is
t = -b/(2a)
t = -30/(2*(-2))
t = -30/(-4)
t = 7.5 secs
.
s = -2.7t^2+30t+6.5
s = -2.7(7.5)^2+30(7.5)+6.5
s = 79.625 feet (max height)