reflection of a quadratic function over the x-axis

1. Understand the transformation: A reflection of a function $f(x)$ over the $x$-axis is represented by the function $-f(x)$. This means for every input $x$, we calculate the original function value $f(x)$ and then negate it.

1. Define the reflected function: Given $f(x) = (x - 1)^2$, the reflected function is $-f(x) = -(x - 1)^2$.

1. Calculate the values for the table: We need to evaluate $-f(x)$ for $x = 0$, $x = 1$, and $x = 2$.

- For $x = 0$:
$f(0) = (0 - 1)^2 = (-1)^2 = 1$
$-f(0) = -(1) = -1$

- For $x = 1$:
$f(1) = (1 - 1)^2 = (0)^2 = 0$
$-f(1) = -(0) = 0$

- For $x = 2$:
$f(2) = (2 - 1)^2 = (1)^2 = 1$
$-f(2) = -(1) = -1$

4. Complete the table: Based on the calculations, the table values are:
- When $x = 0$, $-f(x) = -1$
- When $x = 1$, $-f(x) = 0$
- When $x = 2$, $-f(x) = -1$