How do we go from a general form to a canonique form (2nd degree)

How do we go from a general form to a canonique form (2nd degree)

see: https://www.youtube.com/watch?v=5Yke-3yNYcA

I believe general form is

$$y=ax^2+bx+c$$

I do not know what canonique form is.  

tell me what it is and I will show you how to do the conversion.