Question

A rocket is launched into the air and follows the path, h (t) = -3 * t^2 + 12 * t

Answer 1

check the picture below.

so, the rocket will come back to the ground when h(t) = 0, thus

$\bf h(t)=-3t^2+12t\implies \stackrel{h(t)}{0}=-3t^2+12t\implies 0=-3t(t-4)\\\\[-0.35em]~\dotfill\\\\0=-3t\implies 0=t\impliedby \textit{0 seconds when it took off from the ground}\\\\[-0.35em]~\dotfill\\\\0=t-4\implies 4=t\impliedby \textit{4 seconds later, it came back down}$