What is the maxiumum height of the rocket? (projectile motion)?

If you graph this equation on the t-h plane (instead of x-y), it will be a parabola. The vertex of the parabola in this case has t-coordinate = -b/(2*a), where a is the coefficient of t^2 and b is the coefficient of t. Substituting in numbers in this case, we get -(49)/(2*(-4.9))=10/2=5, which means that when t=5 seconds, the rocket will be at its maximum height (maximum because -4.9<0). Since you want the height, substitute 5 for t in the equation and solve for h.