Skip to content
Math

Quadratic: Formats, File Types, and Size Limits

An overview of the Equation Solver's inputs — the coefficients a, b, and c — and the results it returns.

Published August 28, 20264 min read
Share:

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

InputMeaningExample (x² − 5x + 6 = 0)
aCoefficient of x²1
bCoefficient of x−5
cConstant term6

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.

Free tools to do it now

Frequently asked questions

What does a, b, and c represent?

In ax² + bx + c = 0, a is the x² coefficient, b the x coefficient, and c the constant term.

Can b or c be zero?

Yes. Equations like x² − 4 = 0 (b = 0) or x² − 4x = 0 (c = 0) are valid.

Why must a be non-zero?

If a = 0 the equation is linear, not quadratic, so the quadratic formula and parabola analysis no longer apply.

Get notified when we add new tools

One email when a useful tool or guide goes live. No spam, unsubscribe anytime.

Your email is saved locally on this device and is never sent to a server yet.

Back to all guides