What is this method and how would I apply it to this expression y= -3x(squared) + 6x - 7 ion vertex form

You can use the general formula for this by plugging in your values for a,b, and c.

a(x+\frac{b}{2a})^{2}+\underbrace{c-\frac{b^{2}}{4a}}_{\text{constant term}}

a=-3, b=6, c=-7