AHSME 1951 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: $\mathrm{(A) \ have\ a\ maximum } \mathrm{(B) \ have\ a\ minimum}$ $\mathrm{(C) \ be\ tangent\ to\ the\ x-axis}$ $\mathrm{(D) \ be\ tangent\ to\ the\ y-axis}$ $\mathrm{(E) \ lie\ in\ one\ quadrant\ only}$