The standard form of a parabola looks like a quadratic equation. So I guess you want the standard form of a parabola.
Complete the square:
y=x2-12x+32 = (x2-12x+36)-36+32 = (x-6)2-4.
y+4=(x-6)2 is the standard form. The vertex of the parabola is seen to be (6,-4) from this format.