QUADRATIC FUNCTIONS: Completing the Square

1K 22 6
                                    


Welcome to an introduction to quadratic equations! This lesson hinges on the assumption that you, reader, already know the very basics: algebraic arithmetic, basic exponents, and the quadratic formula. If you do, then excellent! Let's move forward.

To begin with, all quadratic equations come in a form like this: 

To begin with, all quadratic equations come in a form like this: 

Oops! This image does not follow our content guidelines. To continue publishing, please remove it or upload a different image.


Where a, b, and c are variables and x is another that you generally have to solve for. This equation equals to zero.

The first main topic you learn in A-level math under quadratic equations is the completion of the square. It relies on this expansion:

Now, in case you don't know how this expansion comes about:

Oops! This image does not follow our content guidelines. To continue publishing, please remove it or upload a different image.

Now, in case you don't know how this expansion comes about:

Coming back to the topic - say we have a square with side length a

Oops! This image does not follow our content guidelines. To continue publishing, please remove it or upload a different image.

Coming back to the topic - say we have a square with side length a.

The area of this square is going to be a x a, or a^2.

Oops! This image does not follow our content guidelines. To continue publishing, please remove it or upload a different image.
MATHEMATICSWhere stories live. Discover now