First, consider that a quadratic equation in vertex form is given by:

where a is the leading coefficient and (h,k) is the vertex of the curve.
You have the following equation:

In this case, the leading coefficient is a = 1.
The vertex is determined as follow:
Use the following formula to find h:

where we have used b = -6.
Now, to find k use:

Then, h = 3 and k = 3.
By replacing the values of a, h and k, you obtain:

The previous result is the given equation in vertex form.