Equation Solver: inputs and results
Because the Equation Solver works from typed numbers, the "formats" here describe its inputs — the coefficients a, b, and c — and what it returns.
Input fields
| Input | Meaning | Example (x² − 5x + 6 = 0) |
|---|---|---|
| a | Coefficient of x² | 1 |
| b | Coefficient of x | −5 |
| c | Constant term | 6 |
Input rules
- a must be non-zero (otherwise the equation is linear, not quadratic)
- b and c may be any real number, including zero
- Negative values use the minus sign, e.g., −5
- Decimals are supported for all coefficients
What the solver returns
- Real roots — the solutions, if real, based on the discriminant
- Vertex — the turning point (x, y) of the parabola
- Axis of symmetry — the vertical line x = −b / 2a
- Parabola chart — a plotted curve showing shape and direction
About the discriminant
The value b² − 4ac decides the outcome: positive gives two distinct real roots, zero gives one repeated root, and negative gives no real roots.
Verdict
With just three coefficients, the Equation Solver returns roots, vertex, axis, and a chart — a complete solution to any quadratic.