Completing the Square Calculator

Completing the square rewrites a x^2 + b x + c as a squared bracket plus a constant, which is where the vertex form and the quadratic formula both come from. Enter the three coefficients and the result gives the vertex form, the vertex, the axis of symmetry and the roots, with the working written out one line at a time. The steps show the factoring, halving b, squaring it, and adding and subtracting that square, so the method can be followed rather than just its answer copied. Halves and thirds are printed as exact fractions, because that is where the arithmetic usually goes wrong.