If you simplify this into the general form of an equation for an x^2 parabola, what you get is y = - .25x^2. Because there is no up or down movement, nor is there any side to side movement, this parabola is still sitting at the origin. The - out front turns it upside down, and the value of 1/4 makes it open up wider that its parent function y = x^2. So the axis of symmetry is x = 0 which is actually the equation for the line of symmetry. The axis of symmetry is the y axis because the function opens up evenly on each side of the y axis.
