Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Completing the Square

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Completing the square of a quadratic function is useful for solving the equation , for plotting the graph of the function, or for finding the center of the circle (or other conic section) that is the graph of .

[more]

Here is how completing the square works in words:

(1) Factor out from the first two terms, .

(2) Add the constant term in order to be able to factor as a square. Subtract from to keep equality.

(3) Factor to get the result, .

Here it is in symbols:

[less]

Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA

Snapshots

Details

In calculus, completing the square lets you use substitution to change integrals involving quadratics to some standard form. For example,

and or .

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send