Question

1. write the equation that models the height of the roller coaster.

start by writing the equation of the circle. (recall that the general form of a circle with the center at the origin is x² + y² = r². (10 points)

now solve this equation for y. remember the roller coaster is above ground, so you are only interested in the positive root. (10 points)

Explanation:

Step1: Write the circle equation

The general form of a circle with center at the origin is $x^{2}+y^{2}=r^{2}$.

Step2: Solve for y

Subtract $x^{2}$ from both sides: $y^{2}=r^{2}-x^{2}$. Then take the square - root of both sides. Since the roller coaster is above ground, we take the positive root. So $y = \sqrt{r^{2}-x^{2}}$.

Answer:

$y=\sqrt{r^{2}-x^{2}}$