Quadratic Equation Calculator
Solve a quadratic equation ax² + bx + c = 0 and get the discriminant, roots and vertex.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
The calculator uses the quadratic formula to find real roots when they exist. The discriminant shows whether there are two, one repeated, or no real roots; the calculator also gives the parabola’s vertex.
Worked example
calculated with the default values below
Coefficient a 1 · Coefficient b -3 · Constant c 2 Discriminant 1.0000 · First root 2 · Second root 1 · Vertex x 1.500000 · Vertex y -0.250000 · Sum of roots 3.000000
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
D = b² − 4ac; x = (−b ± √D) ÷ 2a when D ≥ 0
- a
- Coefficient a
- b
- Coefficient b
- c
- Constant c
- D
- Discriminant
- x
- Real roots
- xᵥ
- Vertex x-coordinate
- yᵥ
- Vertex y-coordinate
a must be nonzero. If D < 0, the real-root fields are blank because no real roots exist.
Frequently asked questions
What happens if the discriminant is negative?
A negative discriminant means there are no real roots, so the root fields are left blank. The calculator rejects a = 0 because the equation is then not quadratic.