1. The problem asks to find the zeros of the function $f(x) = x^2 - 2x + 1$. 2. To find the zeros, we solve the equation $f(x) = 0$, which means: $$x^2 - 2x + 1 = 0$$ 3. This is a quadratic equation. We can try to factor it: $$x^2 - 2x + 1 = (x - 1)^2$$ 4. Setting the factor equal to zero: $$(x - 1)^2 = 0$$ 5. This implies: $$x - 1 = 0$$ 6. Solving for $x$: $$x = 1$$ 7. Therefore, the function has one zero at $x = 1$, but since it is a repeated root (multiplicity 2), the function touches the x-axis at this point. Final answer: The function $f(x) = x^2 - 2x + 1$ has 1 zero at $x = 1$.