Use the table to answer the question.

Question

x f(x)
−1
0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4 . Which of the given x values produces the largest output for the function?

(1 point)
Responses

x=−1
x equals negative 1

x=0
x equals 0

x=1
x equals 1

x=2

Answer 1

To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate the output \( f(x) \) for each given \( x \) value:

1. For \( x = -1 \): \[ f(-1) = -((-1 + 1)^2) + 4 = -(0^2) + 4 = 0 + 4 = 4 \]

2. For \( x = 0 \): \[ f(0) = -((0 + 1)^2) + 4 = -1^2 + 4 = -1 + 4 = 3 \]

3. For \( x = 1 \): \[ f(1) = -((1 + 1)^2) + 4 = -2^2 + 4 = -4 + 4 = 0 \]

4. For \( x = 2 \): \[ f(2) = -((2 + 1)^2) + 4 = -3^2 + 4 = -9 + 4 = -5 \]

Now we can 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, examining the outputs:

• \( f(-1) = 4 \)
• \( f(0) = 3 \)
• \( f(1) = 0 \)
• \( f(2) = -5 \)

The largest output occurs at \( x = -1 \) where \( f(-1) = 4 \).

Therefore, the answer is:

x = -1