Question 349018
Because
s(t)= -16t^2+ 48t
is a "quadratic" -- a parabola that opens downwards
The max height will be at the vertex.
.
The "time" (t) when it reaches the max is the "axis of symmetry":
t = -b/(2a) = -48/(2*(-16)) = -48/(-32) = 1.5 seconds
.
Height, then is found by plugging the above back into:
s(t)= -16t^2+ 48t
s(1.5)= -16(1.5)^2+ 48(1.5)
s(1.5)= -16(2.25)+ 48(1.5)
s(1.5)= -36+ 48(1.5)
s(1.5)= -36+ 72
s(1.5)= 36 feet (this is what they're looking for)