Question

A highway underpass is parabolic in shape as shown on the diagram below. The curve of the underpass can be modelled by the quadratic function

Answer 1

The curve of the underpass can be modelled by the quadratic function

$$h(x)=50-0.02x^2$$

The highest point occurs at the vertex

$$x_v=-\dfrac{0}{2(-0.02)}=0$$

$$h_v=h(0)=50$$

The vertex is $(0, 50)$ so the highest point of the underpass is 50 feet.

Find the distance between the two x-intercepts.

$$h(x)=0=>50-0.02x^2=0$$

$$x^2=2500$$

$$x=\pm50$$

The distance between the two intercepts is the width of the underpass, which is 100 feet.