User:Thiênio E. da Costa/Completing the square

This animation shows the process of completing the square. (Details, animated GIF version)

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form

$ax^{2}+bx+c\,\!$

to the form

$a(\cdots \cdots )^{2}+{\mbox{constant}}.\,$

In this context, "constant" means a number that does not depend on x. The expression inside the parenthesis is of the form (x + constant). Thus

$ax^{2}+bx+c\,\!$

is converted to

$a(x+h)^{2}+k\,$

for some values of h and k.

Completing the square is used in

• solving quadratic equations;
• graphing quadratic functions;
• evaluating integrals in calculus;
• finding Laplace transforms.

In mathematics, completing the square is often applied in any computation involving quadratic polynomials. Completing the square is also used to derive the quadratic formula.

External links

• How to Complete the Square, Education Portal Academy

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