Question

X
-1 f (x)
0
1
2

Finish creating the input output table for the function f (x) = -(x + 1)^2 + 4

Answer 1

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

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 an input-output table:

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

This is the completed input-output table for the function \( f(x) = -(x + 1)^2 + 4 \).