Quadratic Formula Calculator

A quadratic equation has the form ax^2 + bx + c = 0, and the quadratic formula gives its roots directly from the three coefficients. Enter a, b and c to get the discriminant, both roots, the vertex and the axis of symmetry. A negative discriminant means the parabola never crosses the horizontal axis, so the roots come back as a complex conjugate pair. Coefficient a cannot be zero, because the equation would then be linear rather than quadratic.