Quadratic Formula Calculator
Enter the coefficients of ax² + bx + c = 0 to find the roots, discriminant, and vertex.
How the quadratic formula works
Any quadratic equation ax² + bx + c = 0 is solved with x = (−b ± √(b² − 4ac)) / (2a). The part under the square root, b² − 4ac, is the discriminant: it decides whether you get two real roots, one repeated root, or a complex pair. The vertex of the parabola sits at x = −b / 2a.
Frequently asked questions
What is the quadratic formula?
For ax² + bx + c = 0, the roots are x = (−b ± √(b² − 4ac)) / (2a). This calculator plugs your values of a, b, and c into that formula and simplifies.
What does the discriminant tell me?
The discriminant is b² − 4ac. If it is positive there are two real roots, if it is zero there is one repeated real root, and if it is negative the two roots are complex conjugates.
Why must a not be zero?
If a is zero the x² term disappears and the equation becomes linear (bx + c = 0), not quadratic, so the quadratic formula no longer applies.