When a function \( f(x) \) is reflected over the x-axis, the new function can be obtained by negating the original function.
Given the function:
\[ f(x) = (x - 1)^2 \]
To reflect this function over the x-axis, we change the sign of \( f(x) \):
\[ f(x) = -(x - 1)^2 \]
Thus, the new function after reflection over the x-axis is:
\[ f(x) = -(x - 1)^2 \]