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=1
x equals 1

x=2
x equals 2

x=0

Answer 1

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

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

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 summarize the values:

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

Based on these calculated outputs, the largest output occurs at \( x = -1 \), where \( f(-1) = 4 \).

So the answer is: x = -1