1955 AHSME Problem 28

On the same set of axes are drawn the graph of y=ax^2+bx+c and the graph of the equation obtained by replacing x by -x in the given equation. If b \neq 0 and c \neq 0 these two graphs intersect:

\begin{array}{l} \textbf{(A)}\ \text{in two points, one on the x-axis and one on the y-axis}\\ \textbf{(B)}\ \text{in one point located on neither axis}\\ \textbf{(C)}\ \text{only at the origin}\\ \textbf{(D)}\ \text{in one point on the x-axis}\\ \textbf{(E)}\ \text{in one point on the y-axis} \end{array}

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