Math
Complex number modulus
Find the distance of a complex number from the origin of the complex plane.
Calculators / Math / Complete the square
Complete the square calculator
Rewrite a quadratic as a(x − h)² + k using its vertex and outer coefficient.
On this page
Vertex x3
Vertex y-4
Outer coefficient1
Calculator controls
How to calculate
Rewrite a quadratic as a(x − h)² + k using its vertex and outer coefficient.
Vertex x = -b/(2*a); Vertex y = c-b^2/(4*a); Outer coefficient = a
Worked example
Quadratic coefficient: 1; Linear coefficient: -6; Constant term: 5.
Vertex x: 3 ; Vertex y: -4 ; Outer coefficient: 1 .
Assumptions and limits
The quadratic coefficient must be nonzero. Vertex h and k describe the completed-square form; this tool does not compute complex roots.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Rewrite a quadratic as a(x − h)² + k using its vertex and outer coefficient.
When this tool is useful
Vertex x = -b/(2*a); Vertex y = c-b^2/(4*a); Outer coefficient = a
Understanding your inputs
| Input | What to enter |
|---|---|
| Quadratic coefficient | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Linear coefficient | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Constant term | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
The quadratic coefficient must be nonzero. Vertex h and k describe the completed-square form; this tool does not compute complex roots.
How is the result calculated?
Vertex x = -b/(2*a); Vertex y = c-b^2/(4*a); Outer coefficient = a