Solve any quadratic equation of the form ax squared plus bx plus c equals zero. Enter the three coefficients a, b and c, and the calculator applies the quadratic formula to find the roots, correctly handling all three cases: two distinct real roots, one repeated real root, or a pair of complex conjugate roots when the discriminant is negative. It also shows the discriminant itself and the coordinates of the vertex, which together describe the whole parabola. Seeing the discriminant makes it clear why an equation has the number of real solutions it does. This is a staple of algebra and physics. Enter your coefficients and the full solution appears instantly, computed locally in your browser with nothing sent anywhere.