y = (x-1)^2 + 2 is a parabola (from the square of the (…) container. The multiplier of the (…) is 1 so it is upright and neither stretched nor shrunk. The x-1 tells you that it is shifted <right> 1 step and the right most +2 tells you that parabola has been shifted <up> 2 steps.
The vertex of x^2 is at (0, 0) so the shift means that the vertex has been moved x from 0 to +1 and y from 0 to +2. That means the unshifted parabola vertex that was at (0, 0) is moved to vertex location (1, 2).