1957 AHSME Problem 40

If the parabola y = -x^2 + bx - 8 has its vertex on the x-axis, then b must be:

\begin{array}{l} \textbf{(A)}\ \text{a positive integer}\qquad \\ \textbf{(B)}\ \text{a positive or a negative rational number}\qquad \\ \textbf{(C)}\ \text{a positive rational number}\qquad\\ \textbf{(D)}\ \text{a positive or a negative irrational number}\qquad\\ \textbf{(E)}\ \text{a negative irrational number} \end{array}

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