We have this form : y = ax^2 + bx + c .....so......
y = x^2 - 6x + 7
The x coordinate of the vertex is given by -b/ 2a where b = -6 and a = 1
So ..... - (-6)/ 2(1) = 6/2 = 3 and this is the x coordinate of the vertex
To find the y coordinate......just plug "3" back into the function....and we have
(3)^2 - 6(3) + 7 =
9 - 18 + 7 =
-2
So the vetex is (3, -2)
Here's the graph that confirms this : https://www.desmos.com/calculator/2h7phyucv7