Question

the quadratic regression graphed on the coordinate grid represents the height of a road surface x meters from the center of the road.
road surface height
what does the graph of the regression model show?
the height of the surface decreases from the center out to the sides of the road.
the height of the surface increases, then decreases, from the center out to the sides of the road.
the height of the surface increases from the center out to the sides of the road.
the height of the surface remains the same the entire distance across the road.

Explanation:

A quadratic regression graph (parabola) is shown. The vertex (highest point) is at the center (\(x = 0\)). As \(x\) (distance from the center) increases, the \(y\)-value (height) first increases (from \(x=- 6\) to \(x = 0\)) and then decreases (from \(x = 0\) to \(x=6\)). But wait, looking at the graph more carefully, actually, since it's a quadratic regression, and the parabola opens down - ward (as we can see from the shape). When moving from the center (\(x = 0\)) outwards (increasing \(|x|\)), the height \(y\) decreases.

Answer:

The height of the surface decreases from the center out to the sides of the road.