### Home > INT3 > Chapter 10 > Lesson 10.1.5 > Problem 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*= –4.9*t*^{2}+ 49*t*+ 11.27, where time,*t*, is in seconds. Homework Help ✎What is the height of the platform?

What is the maximum height the firework reaches?

How many seconds until it hits the ground?

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*(*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).

*h*(*x*) = -4.9(*t* − 5)² + 133.77

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