The formulae for a parabola is:

Ax^2+Bx+C=Y

If Y=0 then X = (-B +/- SQUROOT(B^2-4AC))/2A

Except for the point on the axis of symmetry, each value for Y will have two (extraneous) answers.

In figuring the axis of symmetry, we know that it lies midway between the positive and negative values of the equation.

Simply adding these values together and dividing by two will get us the "average" value.

((-B + SQUROOT(B^2-4AC))/2A + (-B - SQUROOT(B^2-4AC))/2A)/2

The positive and negative cases cancel out, leaving

(-2B/2A)/2

Hence the equation for the axis of symmetry is:

-B/2A