\(h(t)=20-16t^2+32t \\ \Downarrow \\ h(t)=-16t^2+32t+20 \\ \\
a=-16 \\ b=32\)
The maximum height is the y-coordinate of the vertex (x,y) of the parabola.
First find the x-coordinate using the formula:
\(x=\frac{-b}{2a}=\frac{-32}{2 \times (-16)}=\frac{-32}{-32}=1\)
Now plug the value into the equation and find the y-coordinate:
\(y=h(x)=h(1)=-16 \times 1^2+32 \times 1+20=-16+32+20=36\)
The maximum height is 36 feet.
