1958 AHSME Problem 22

A particle is placed on the parabola y = x^2 - x - 6 at a point P whose y-coordinate is 6. It is allowed to roll along the parabola until it reaches the nearest point Q whose y-coordinate is -6. The horizontal distance traveled by the particle (the numerical value of the difference in the x-coordinates of P and Q) is:

\textbf{(A)}\ 5\qquad \textbf{(B)}\ 4\qquad \textbf{(C)}\ 3\qquad \textbf{(D)}\ 2\qquad \textbf{(E)}\ 1

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