What is y equals x to the second power minus 6x +7 in vertex form

Y= x²- 6x +7 

Vertex form is y= a(x-h)² +k 

The vertex form of this equation would be y= (x-3)²- 2  because if we transform to the standard form it would be equal to y= x²-6x+7  so we just have to complete the perfect square (which means to complete, following the rules, with the numbers that will make this equation right in the standard form). 

How our x² is equal to 1 on our standard form (like it is not 2x², it is just x²), our ''a'' on the vertex form is 1 so we simply don't have to write the 1 in front of it so it stays y= 1(x-3)² -2 or y=(x-3)²-2.  Look how it works: (x-3)²  we use the rule of a²+2ab+c² which is the square of the first x² plus  two times the first term times the second -6x plus the square of the last term (-3)² =  9   so we have x²-6x+9 - 2 that gives us the standard form x²-6x+7. So, that's true that the vertex form is y=(x-3)²-2