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=0

x equals 0
x=1
x equals 1
x=2
x equals 2
x=−1

Answer 1

To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate \( f(x) \) for each of the given \( x \) values: -1, 0, 1, and 2.

Let's calculate each value:

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

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

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

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

Now we can summarize the values in the table:

\[ \begin{array}{c|c} x & f(x) \ \hline -1 & 4 \ 0 & 3 \ 1 & 0 \ 2 & -5 \ \end{array} \]

Now we can identify which \( x \) value produces the largest output:

• The maximum output is \( f(-1) = 4 \).

Thus, the response to the question is: \( x = -1 \) produces the largest output for the function.