1998 AHSME Problem 14

A parabola has vertex of (4,-5) and has two x-intercepts, one positive, and one negative. If this parabola is the graph of y = ax^2 + bx + c, which of a,b, and c must be positive?

\mathrm{(A) \ } \text{only}\ a \qquad \mathrm{(B) \ } \text{only}\ b \qquad \mathrm{(C) \ } \text{only}\ c \qquad \mathrm{(D) \ } a\ \text{and}\ b\ \text{only} \qquad \mathrm{(E) \ } \text{none}

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