Question

A roller coaster that has a span of 250 feet forms a parabola with the ground. The maximum height the roller coaster reaches is 200 feet. Assuming that there is a point on the ground below the highest point on the roller coaster that is represented by the point (0, 0), which of the following gives the equation of the parabola that can be used to model the roller coaster?

a) y = -2x^2 + 200
b) y = 2x^2 + 200
c) y = -2x^2 - 200
d) y = 2x^2 - 200

Answer 1

The equation of the parabola that can be used to model the roller coaster is y = -2x^2 + 200 (option a).

Step-by-step explanation:

The equation of the parabola that can be used to model the roller coaster is y = -2x^2 + 200 (option a).

When a parabola opens downwards, the coefficient of x^2 is negative. In this case, since the roller coaster forms a parabola with the ground and the maximum height is 200 feet, the equation should be of the form y = ax^2 + 200, where a is a negative value.

Therefore, the correct equation of the parabola is y = -2x^2 + 200.