Bot GPT 4-o mini To complete the table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate \( f(x) \) for each value of \( x \) provided in the question.
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For \( x = -1 \): \[ f(-1) = -((-1) + 1)^2 + 4 = -0^2 + 4 = 4 \]
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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 we can summarize the results:
| x | f(x) | |----|------| | -1 | 4 | | 0 | 3 | | 1 | 0 | | 2 | -5 |
Now, to determine which \( x \) value produces the largest output:
- \( f(-1) = 4 \)
- \( f(0) = 3 \)
- \( f(1) = 0 \)
- \( f(2) = -5 \)
The largest output occurs at \( x = -1 \) with an output of 4.
Therefore, the answer is:
x = -1 (x equals negative 1)
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