Help with Quadratics problem PLEASE?

The question is flawed, but anyway: in h = at^2 + bt + c, the original height is c, so the tip of the nose cone is 2 metres above ground at t = 0; that should tell you how tall it is. To find the time when the height is greatest means to find the (first) coordinate of the vertex. Many ways to do this, but a short cut from calculus is t = ( -13)/(2)(-3) don't worry about why this shortcut works. For max height take the value of t I just gave you and put it in to the equation and work it out. For total time of flight, set h to zero, then solve (quadratic equation) and take the positive answer.