### Home > INT3 > Chapter 10 > Lesson 10.1.5 > Problem10-73

10-73.

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 above the ground is given by $h = –4.9t^{2} + 49t + 11.27$, where time, $t$, is in seconds.

1. What is the height of the platform?

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

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

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

$h\left(x\right) = -4.9\left(t − 5\right)^2 + 133.77$

2. What is the maximum height the firework reaches?

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

3. How many seconds until it hits the ground?