Fireworks for the annual $4$^th of July show are launched straight up from a steel platform. The entire show is computer controlled. The height of a particular firework in meters above ground level is given by $h = -4.9t^2 + 50t + 11$, where time, $t$, is in seconds.

1. What is the height of the platform?

   Hint (a):

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

2. How many seconds does it take for the firework to hit the ground?

3. What is the maximum height of the firework?

   Hint (c):

   Complete the square to write the equation in graphing form.

   More Help (c):

   Remember that the vertex of a negatively oriented parabola is also the maximum height of the parabola.
   Therefore, this question is really asking you to find the $y$ component of the vertex.

   Step 1:

   $y = -4.9(t^2 - 10.2t) + 11$

   Step 2:

   $y = -4.9(t - 5.1)^2 + 138.5$

   Answer:

   $y ≈ 138.5$ ft