# Example 2

- Author:
- Walch Education

An amusement park has commissioned the design of a steel roller coaster with a drop section that is modeled by a parabola. Part of the roller coaster’s track will go through an underground tunnel. In this section, the roller coaster will dip feet below ground level. The roller coaster will dip below ground level at a horizontal distance of feet from the peak just before the drop and reemerge to ground level at a horizontal distance of feet from the peak just before the drop. Find an equation of the parabola that describes the drop and the height of the roller coaster at the peak.

- Derive the coordinates of the points on the parabola.
- Establish the linear factors and the equation of the parabola.
- Find the vertex of the parabola.
- Find the value of
. - Find the height of the peak of this section of the roller coaster.