To complete the input-output table for the function \( f(x) = -(x+1)^2 + 4 \), we will calculate \( f(x) \) for each given \( x \) value: -1, 0, 1, and 2.
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For \( x = -1 \): \[ f(-1) = -((-1) + 1)^2 + 4 = -(0)^2 + 4 = 0 + 4 = 4 \]
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For \( x = 0 \): \[ f(0) = -(0 + 1)^2 + 4 = -(1)^2 + 4 = -1 + 4 = 3 \]
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For \( x = 1 \): \[ f(1) = -(1 + 1)^2 + 4 = -2^2 + 4 = -4 + 4 = 0 \]
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For \( x = 2 \): \[ f(2) = -(2 + 1)^2 + 4 = -3^2 + 4 = -9 + 4 = -5 \]
Now let's summarize the results in the table:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -1 & 4 \ 0 & 3 \ 1 & 0 \ 2 & -5 \ \hline \end{array} \]
Now, we can determine which \( x \) value produces the largest output for the function. The outputs are:
- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)
The largest output is \( 4 \), which corresponds to \( x = -1 \).
Thus, the answer is: x = -1
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