Math & StatisticsFormula-based · Runs in your browser

Quadratic Formula Calculator

Find real or complex roots, discriminant, vertex, and axis of symmetry.

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Inputs

Enter the values you know. Optional fields may be left empty.

Local save controls below
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Result

Updates as valid inputs change.

Calculated locally
Roots
Discriminant
Vertex
Axis of symmetry

Saved locally, explained clearly

Drafts, calculations, scenarios, and workflow progress stay in this browser unless you export them.

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Calculation steps

Follow what happened from the selected formula to the displayed answer.

Show substituted values and intermediate working
Calculate current inputs to see the working.
  1. 1

    Formula selected

    The calculator uses the following formula or method.

    x = (−b ± √(b² − 4ac)) ÷ 2a

  2. 2

    Values entered

    Your values are placed into the calculation.

    Enter values to see what is used in this step.

  3. 3

    Result calculated

    The formula or method produces the following result values.

    Results will appear after a successful calculation.

  4. 4

    Answer formatted

    Displayed values are rounded and formatted using each output’s configured precision.

Scenario comparison

Save working scenarios, then select two or three to compare. Formula versions and inputs remain visible.

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Recent calculations

Successful calculations are retained locally according to your privacy settings.

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Data and privacy

How it works

The discriminant decides whether the roots are two real values, one repeated real value, or a complex pair.

Input query strings and outputs

Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.

Input query strings

3
  • ?a= a

    Number · Required · Default: 1

  • ?b= b

    Number · Required · Default: -3

  • ?c= c

    Number · Required · Default: 2

Outputs

4
  • roots Roots

    Text · Primary output

  • discriminant Discriminant

    Number

  • vertex Vertex

    Text

  • axis Axis of symmetry

    Number

Equation form

Inputs represent ax² + bx + c = 0.

Sources
  • No external reference is listed for this calculator. Its formula and variable definitions are shown above.
Limitations
  • Results depend on the selected method and input assumptions. Displayed decimals may be rounded; retain appropriate precision for later calculations.