Question

Engineering The height in feet of the curved arch support for a bridge over a creek can be modeled by f(x)=-0.628x (squared)+4.5x, Where x is the horizontal distance in feet from where the arch support enters the water. If there is a flood that raises the level of the creek by 5.5 feet, will the top of the arch support be above the water? Explain

Answer 1

yes

Explanation:

You want to know if an arch support whose height is modeled by f(x) = -0.628x² +4.5x will remain above water if the creek rises 5.5 feet in a flood.

Vertex

The vertex of the arch is found by putting the equation into vertex form:

f(x) = -0.628(x² -7.1656x +12.8365) +8.0613 . . . . . complete the square

f(x) = -0.628(x -3.5828)² +8.0613

The top of the arch support is about 8.06 feet above the water, so it will remain above the water when a flood raises the level of the creek.