Question

The quadratic function y = -x2 + 10x - 8 models the height of a trestle on a bridge. The x-axis represents ground level.

To find where the section of the bridge meets ground level, solve 0 = -x2 + 10x - 8.

Where does this section of the bridge meet ground level?

Answer 1

Set y = 0: 0 = -x^2 + 10x - 8 -> x^2 - 10x + 8 = 0.

Using the quadratic formula:
x = [10 ± sqrt(100 - 32)]/2 = [10 ± sqrt(68)]/2 = 5 ± sqrt(17).

So the bridge meets ground at x = 5 − sqrt(17) ≈ 0.877 and x = 5 + sqrt(17) ≈ 9.123 (points (5 ± sqrt(17), 0)).