1951 AHSME Problem 16

If in applying the quadratic formula to a quadratic equation

f(x) \equiv ax^2 + bx + c = 0,

it happens that c = \frac{b^2}{4a}, then the graph of y = f(x) will certainly:

\begin{array}{l} \textbf{(A)}\ \text{have a maximum}\qquad\textbf{(B)}\ \text{have a minimum}\qquad\textbf{(C)}\ \text{be tangent to the x-axis}\\ \qquad\textbf{(D)}\ \text{be tangent to the y-axis}\qquad\textbf{(E)}\ \text{lie in one quadrant only} \end{array}

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