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Completing the Square Calculator — result sheet
Convert a quadratic polynomial into vertex form and return its vertex from coefficients.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: ax²+bx+c=a(x−h)²+k, where h=−b/(2a) and k=c−b²/(4a).
The vertex coordinates and completed-square coefficients are returned without requiring symbolic expression parsing.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Quadratic coefficient a — minimum -1000000; maximum 1000000
- Linear coefficient b — minimum -1000000; maximum 1000000
- Constant c — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Quadratic coefficient a | 2 |
| Linear coefficient b | -8 |
| Constant c | 3 |
Vertex = (2, −5); form =2(x−2)²−5.
Assumptions and limits
- The quadratic coefficient a is nonzero and all coefficients are finite.
- The polynomial is interpreted over the real numbers.
- Roots, graphing, symbolic factoring, and domain restrictions from a wider expression are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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