Which is the graph of f(x)=x^2-2x+3

The graph of this function would be a positive quadratic graph, so a curve with ends that go upwards, with a turning point at the top of the curve at (1, 2).

If we complete the square of this function, we get (x - 1)² + 2, which tells us that the turning point is (1, 2) as to make the bracket equal 0, x has to be 1, and 2 is the only number outside of the bracket.
I hope this helps!