# Completing the Square Calculator

> Rewrite a quadratic in vertex form and calculate its vertex and roots.

Page: https://askcalculators.com/calculator/completing-the-square-calculator/
Definition: https://askcalculators.com/calculator/completing-the-square-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/completing-the-square-calculator/schema.json
Version: 1.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/completing-the-square-calculator/?a=1&b=6&c=5

## Inputs
- a: Coefficient a; type=number; required; default=1
- b: Coefficient b; type=number; required; default=6
- c: Coefficient c; type=number; required; default=5

## Outputs
- vertexForm: Vertex form; format=text; primary
- vertex: Vertex (h, k); format=text
- discriminant: Discriminant; format=number
- roots: Roots; format=text

## Formula
ax² + bx + c = a(x + b/2a)² + c − b²/4a

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.