A bridge is sketched in the coordinate plane as a parabola represented by the equation h=40-0.01x2, where h refers to the height, in feet, of the bridge at a location of x feet from the middle of the bridge. The bridge starts and ends at the x-intercepts of the parabola. What is the length of this bridge?

The length of the bridge is 126.492 feet.

Step-by-step explanation:

Let , where is the position from the middle of the bridge, measured in feet, and is the height of the bridge at a location of x feet, measured in feet. In this case, the length of the bridge is represented by the distance between the x-intercepts of the parabola, which we now find by factorization:

(Eq. 1)

Given that the parabola is symmetrical with respect to y-axis, then the length is two times the magnitude of the value found above, that is:

The length of the bridge is 126.492 feet.

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