Completing the Square - how to do it
home | courses | topics | theorems | starters | worksheets | timeline | KS3 | KS4 | KS5
A very nice way of solving quadratic equations is through 'completing the square'. It is nice because it is a relatively easy method, and it also gives you some information about the graph of the quadratic in question.
Perfect Squares are expressions such as these:
Every quadratic expression can be written as
Let's say you have a usual quadratic of the form
, where 
You need to use half of b , so let us introduce a value p such that 
.
Re-write your equation as
Because neither p 2 nor c have x 'attached' to them, you can tidy the equation up and that will be the completed square of the original equation.
You can also use the completed square form to sketch the graph of a quadratic faster. The information given by the completed square form is
This is useful not only for finding the zeros (roots) of the quadratic, but also because you can then easily sketch it.
The vertex of parabola will have coordinates (- p,q ); its axis of symmetry will be x = -p . It will be U (valley) shaped if a > 0, and 'hill' shaped if a < 0.
a > 0
a < 0
artefacts | numerals | concepts | people | places | pythagoreans | egyptians | babylonians
_____________________________________________________________________________________________________________________
Acknowledgements | Copyright | Contact | Mission Statement | Tell a friend about this site