In order to graph a parabola, we need to find several pieces of information, including the vertex. One way to find the vertex of a parabola is to turn the standard form of the quadratic equation into vertex form by completing the square. The primary difference between solving a quadratic by completing the square and putting an equation into vertex form is substituting a "y" for the "0" in the initial equation.
Graphing a parabola when you're not dealing with vertex form. So we know how to graph a parabola when we are in vertex form and we know what these transformations are. This k is going to move the graph up and down, this h is going to move everything side to side and this a is just going to affect the direction and the shape, how steep or narrrow our parabola is.
The problem is when we have something in standard form, x squared minus 4x+6. We don't know how to deal with these transformations, so what we have to do is somehow take this quadratic equation and put it into this form, and how we do that is by completing the square.