2003 AMC 12A Problem 19

A parabola with equation y=ax^2+bx+c is reflected about the x-axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of y=f(x) and y=g(x), respectively. Which of the following describes the graph of y=(f+g)(x)?

\textbf{(A)}\ \text{a parabola tangent to the }x\text{-axis} \textbf{(B)}\ \text{a parabola not tangent to the }x\text{-axis}\qquad\textbf{(C)}\ \text{a horizontal line} \textbf{(D)}\ \text{a non-horizontal line}\qquad\textbf{(E)}\ \text{the graph of a cubic function}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.