Answer
a)This is because $h(t)$ must be positive since it describes the height of the ballet dancer.
b) At $t=T / 2$
c) $4 T^2$
Work Step by Step
a) This is because $h(t)$ must be positive since it describes the height of the ballet dancer. Note that $h(t)=-16 t^2+16 T t=16 t(T-t)$.
b) The times $t=0$ and $t=T$ give the start and end of the jump. The maximum height occurs halfway in between, at $t=T / 2$.
c) The maximum height is
$$
h\left(\frac{T}{2}\right)=16\left(\frac{T}{2}\right)\left(T-\frac{T}{2}\right)=4 T^2 .
$$
