Question

The surface of a road curves like a parabola to allow water to drain off of it. The following equation shows the surface height, y, in feet above the base at a point x feet from the left edge of the road. y=-0.0015x(x-40)

Answer 1

The equation for the surface height of a road designed for water drainage is a quadratic function that represents a downward-opening parabola, useful in understanding its geometric properties and its real-life application.

Step-by-step explanation:

This question is focused on quadratic functions and their applications. More specifically, it looks at a parabolic equation representing the surface height of a road that has been designed for efficient water drainage.

The given quadratic equation, y = -0.0015x(x-40), can be analyzed to understand the features of the parabola, such as its vertex, axis of symmetry, and the direction in which it opens. The equation in its standard form implies that the parabola opens downward (since the coefficient of x^2 is negative), which makes sense for a road surface intended to allow water to drain off.

To properly examine this equation's properties, one could complete the square to find the vertex form or differentiate it to determine the slopes at various points along the surface, applying these concepts to real-world scenarios like water drainage on road surfaces.