Algebra Math Question

Question

A coordinate grid is placed on top of a drawing showing a wire that is hung between two poles. The tops of the poles lies on the x-axis. The wire is attached at the top of the poles. The function f(x) = 4x² + 4x - 15 is used to model the vertical distance the wire hangs from the top of the poles. If x is the horizontal distance measured in yards, how far apart are the poles?

Answer 1

So the best way to answer this question is to find the two roots of the function. Because the tops of the poles are at the x axis, then in essence, the roots of the function are the "poles" and the distance between them would represent the distance between the poles.

The roots of the function are, using the quadratic formula,

-2.5 and 1.5.

The distance between them and therefore the distance between the poles is 1.5 - (-2.5) = 4.0 = 4

I hope I was at least of some help! If my answer is unclear, feel free to message me on Wyzant!