Math & Statistics
Quadratic Equation Calculator
Updated Sep 3, 2026 Reviewed Sep 3, 2026
Solve ax² + bx + c = 0 with stable real or complex roots, then inspect the discriminant, vertex, symmetry axis, intercepts, opening direction, factors, and graph.
Polynomial solver
Enter coefficients a, b, and c
Result
Calculation summary
Enter values to see the result
Your result, breakdown, assumptions, and warnings will appear here.
Function preview
Parabola graph
How to use this calculator
- 1Enter non-zero a and coefficients b and c.
- 2Choose display precision.
- 3Solve to inspect roots, vertex, factors, and graph.
Formula
x = (−b ± √(b² − 4ac)) / 2a
The discriminant determines whether roots are distinct real, repeated, or complex.
Calculation steps
- Compute b² − 4ac.
- Use a cancellation-resistant real-root calculation.
- Evaluate the vertex at x = −b/(2a).
Worked example
For x² − 5x + 6 = 0, the roots are 2 and 3.
Assumptions
- Coefficient a is non-zero.
- Complex roots use i.
- The graph is explanatory, while values are numeric.
Sources
Frequently asked questions
What does the discriminant show?
Its sign identifies the type and count of roots.
Why must a be non-zero?
Otherwise the equation is linear.
Why use a stable method?
It limits digit loss from subtracting similar large values.
When are factors shown?
When real roots exist.
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