Question

X
-1 f (x)
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

Answer 1

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

Let's compute \( f(x) \) for each \( x \):

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

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

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

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

Now, we can summarize the input-output table:

| \( x \) | \( f(x) \) |
|---------|------------|
| -1 | 4 |
| 0 | 3 |
| 1 | 0 |
| 2 | -5 |

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