1. The problem asks to create a table for the reflection about the origin of the function $f(x) = (x + 2)^2 + 1$. 2. The reflection about the origin of a function $f(x)$ is given by $-f(-x)$. 3. First, evaluate $f(x)$ at $x=0, -1, -2$: $$f(0) = (0 + 2)^2 + 1 = 2^2 + 1 = 4 + 1 = 5$$ $$f(-1) = (-1 + 2)^2 + 1 = 1^2 + 1 = 1 + 1 = 2$$ $$f(-2) = (-2 + 2)^2 + 1 = 0^2 + 1 = 0 + 1 = 1$$ 4. Now evaluate $-f(-x)$ at $x=0, 1, 2$: $$-f(-0) = -f(0) = -5$$ $$-f(-1) = -f(-1) = -2$$ $$-f(-2) = -f(-2) = -1$$ 5. The completed table is: $$\begin{array}{c|c|c|c} x & 0 & 1 & 2 \\ \hline -f(-x) & -5 & -2 & -1 \\ \end{array}$$ This shows the values of the reflection about the origin of the function at the given $x$ values.