Question

Complete the table of values for the function f left parenthesis x right parenthesis equals negative one half x squared
.
x
f left parenthesis x right parenthesis equals negative one half x squared
minus4
  
enter your response here
minus2
  
enter your response here
0
  
enter your response here
2
  
enter your response here
4
  
enter your response here
​(Type integers or simplified fractions. Type N if the function is​ u

Answer 1

To complete the table of values for the function \( f(x) = -\frac{1}{2} x^2 \), we simply need to calculate \( f(x) \) for each given value of \( x \). Here are the calculations:

1. For \( x = -4 \):
\[
f(-4) = -\frac{1}{2} (-4)^2 = -\frac{1}{2} \cdot 16 = -8
\]

2. For \( x = -2 \):
\[
f(-2) = -\frac{1}{2} (-2)^2 = -\frac{1}{2} \cdot 4 = -2
\]

3. For \( x = 0 \):
\[
f(0) = -\frac{1}{2} (0)^2 = -\frac{1}{2} \cdot 0 = 0
\]

4. For \( x = 2 \):
\[
f(2) = -\frac{1}{2} (2)^2 = -\frac{1}{2} \cdot 4 = -2
\]

5. For \( x = 4 \):
\[
f(4) = -\frac{1}{2} (4)^2 = -\frac{1}{2} \cdot 16 = -8
\]

Now, we can complete the table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) = -\frac{1}{2} x^2 \\
\hline
-4 & -8 \\
-2 & -2 \\
0 & 0 \\
2 & -2 \\
4 & -8 \\
\hline
\end{array}
\]

So, the completed responses for \( f(x) \) are:

- When \( x = -4 \), \( f(x) = -8 \)
- When \( x = -2 \), \( f(x) = -2 \)
- When \( x = 0 \), \( f(x) = 0 \)
- When \( x = 2 \), \( f(x) = -2 \)
- When \( x = 4 \), \( f(x) = -8 \)