To create an input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will calculate \( f(x) \) for each input value \( x \) given in the table.
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For \( x = -1 \): \[ f(-1) = (-1 - 2)^2 + 3 = (-3)^2 + 3 = 9 + 3 = 12 \]
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For \( x = 0 \): \[ f(0) = (0 - 2)^2 + 3 = (-2)^2 + 3 = 4 + 3 = 7 \]
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For \( x = 1 \): \[ f(1) = (1 - 2)^2 + 3 = (-1)^2 + 3 = 1 + 3 = 4 \]
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For \( x = 2 \): \[ f(2) = (2 - 2)^2 + 3 = (0)^2 + 3 = 0 + 3 = 3 \]
Now we can summarize the results in the input-output table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -1 & 12 \ 0 & 7 \ 1 & 4 \ 2 & 3 \ \hline \end{array} \]