completing the square
we can write
This manipulation is called completing the square  in , or completing the square .
Replacing by , we also have
Here are some applications of this method:
Putting the general equation of a circle, ellipse, or hyperbola into standard form, e.g. the circle
from which it is frequently easier to read off important information (the center, radius, etc.)
since . Here, equality holds if and only if . Thus for all , and if and only if . It follows that has a global minimum at , where .
- 1 R. Adams, Calculus, a complete course, Addison-Wesley Publishers Ltd, 3rd ed.
- 2 Matematiklexikon (in Swedish), J. Thompson, T. Martinsson, Wahlström & Widstrand, 1991.
(Anyone has an English reference?)
|Title||completing the square|
|Date of creation||2013-03-22 13:36:27|
|Last modified on||2013-03-22 13:36:27|
|Last modified by||mathcam (2727)|