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Math — Algebra
Quadratic Formula Calculator
Enter a, b and c to get the roots, the discriminant and the vertex of the parabola.
Roots (x)
—
Solutions of ax² + bx + c = 0.
| Root x₁ | — |
|---|---|
| Root x₂ | — |
| Discriminant | — |
| Vertex | — |
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How the Quadratic Formula Calculator Works
Any quadratic equation in the form ax² + bx + c = 0 can be solved with the quadratic formula. Enter the three coefficients and the calculator returns the roots, the discriminant and the vertex of the parabola.
The discriminant, b² − 4ac, tells you what kind of roots to expect: positive gives two real roots, zero gives one repeated root, and negative gives a pair of complex roots — which the calculator reports in a ± bi form. The vertex, at x = −b/2a, is the turning point of the parabola.
x = (−b ± √(b² − 4ac)) ÷ 2a
Frequently Asked Questions
What does the discriminant tell me?
The discriminant b² − 4ac reveals the roots without solving fully: positive means two distinct real roots, zero means one repeated root, and negative means two complex roots.
What if a is zero?
Then the equation is linear, not quadratic, and the quadratic formula does not apply (it would divide by zero). The calculator flags this case.
What is the vertex?
It is the highest or lowest point of the parabola, located at x = −b/2a. It is useful for graphing and for finding maximum or minimum values.
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