Yes, it does.
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the axis of symmetry
The highest or lowest point of the parabola, it is the point that is closest to the focus. The extreme point lies on the axis of symmetry
y = ax^2 + c where a and c are constants and a is not 0.
"Any light beam moving vertically downwards in the concavity of the parabola (parallel to the axis of symmetry) will bounce off the parabola moving directly towards the focus." http://en.wikipedia.org/wiki/Parabola
The axis of symmetry for a parabola of the form y = ax2 + bx + c is x = -b/2a So the axis is x = -2/2*(-3) or x=1/3