1. **State the problem:** Find the global minimum of the function $$f(x) = x^2 - 2x + 1$$. 2. **Recall the formula and rules:** This is a quadratic function of the form $$ax^2 + bx + c$$ where $$a=1$$, $$b=-2$$, and $$c=1$$. 3. Since $$a > 0$$, the parabola opens upwards, so the vertex represents the global minimum. 4. The vertex $$x$$-coordinate is given by $$x = -\frac{b}{2a}$$. 5. Substitute values: $$x = -\frac{-2}{2 \times 1} = \frac{2}{2} = 1$$. 6. Find the minimum value by evaluating $$f(1)$$: $$f(1) = (1)^2 - 2(1) + 1 = 1 - 2 + 1 = 0$$. 7. **Answer:** The global minimum of $$f(x)$$ is $$0$$ at $$x=1$$.