Question

what does an x-intercept of h(x) represent in the roller coaster context?
a distance where slope is zero
a point of maximum speed on track
a location where track is highest point
a distance where height is zero yards

Explanation:

In the context of a roller coaster modeled by \( H(x) \), the \( x \)-intercept occurs where \( H(x) = 0 \). Since \( H(x) \) likely represents the height of the roller coaster at a horizontal distance \( x \), an \( x \)-intercept is a distance (along the horizontal axis, \( x \)) where the height \( H(x) \) is zero yards. The other options are incorrect: a slope of zero relates to a horizontal tangent (not an intercept), a point of maximum speed or highest point are not defined by \( H(x)=0 \), and "a distance where slope is zero" is unrelated to intercepts.

Answer:

A distance where height is zero yards