Let's complete the table by evaluating the function [tex]\( f(x) = x^2 + 2x \)[/tex] for each given [tex]\( x \)[/tex] value.
### Step-by-Step Solution:
1. For [tex]\( x = -4 \)[/tex]:
- Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( f(x) = x^2 + 2x \)[/tex]:
[tex]\[
f(-4) = (-4)^2 + 2(-4) = 16 - 8 = 8
\][/tex]
2. For [tex]\( x = -2 \)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( f(x) = x^2 + 2x \)[/tex]:
[tex]\[
f(-2) = (-2)^2 + 2(-2) = 4 - 4 = 0
\][/tex]
3. For [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) = x^2 + 2x \)[/tex]:
[tex]\[
f(0) = 0^2 + 2(0) = 0
\][/tex]
4. For [tex]\( x = 2 \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) = x^2 + 2x \)[/tex]:
[tex]\[
f(2) = 2^2 + 2(2) = 4 + 4 = 8
\][/tex]
### Completed Table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-4 & 8 \\
\hline
-2 & 0 \\
\hline
0 & 0 \\
\hline
2 & 8 \\
\hline
\end{tabular}
\][/tex]
So, the function values [tex]\( f(x) \)[/tex] for the given [tex]\( x \)[/tex] values are:
- [tex]\( f(-4) = 8 \)[/tex]
- [tex]\( f(-2) = 0 \)[/tex]
- [tex]\( f(0) = 0 \)[/tex]
- [tex]\( f(2) = 8 \)[/tex]
