Fireworks for the annual Fourth of July show are launched straight up from a steel platform. The launch of the entire show is computer controlled. The height of a particular firework in meters off ground level is given by$h = -4.9t^2 + 49t +11.27$, where time, $t$, is in seconds.

1. What was the height of the platform? What is the maximum height the firework reached? How many seconds until it hit the ground?

   Hint (a):

   Substitute $t = 0$ to find the height of the platform.

   More Help 1(a):

   Use the Quadratic Formula to find the roots. Average them to find the line of symmetry.

   More Help 2(a):

   You have now found the parameter $h$ in the general equation $y = a(x - h)^² + k$.
   The given equation has the same a value, $-4.9$.
   Solve for $k$ by substituting the point you found in part (a).

   Answer (a):

   $h(x) = -4.9(t - 5)^² + 133.77$

2. Rewrite the equation in factored form. Why might factored form of the equation be useful?

   Hint (b):

   The factored form reveals the intercepts. Remember to include the a value in your factored equation.