Question

Graph the function ​f(x)equalsminusxsquaredminus8.
x
​f(x)
minus2
minus1
0
1
2
Question content area bottom left
Part 1
Complete the table of function values below.
x
​f(x)
minus2
  
negative 12
minus1
  
negative 9
0
  
negative 8
1
  
negative 9
2
  
negative 12
Part 2
Use the graphing tool to graph the function.

.
.
.
Question content area right
Part 1
-20
-16
-12
-8
-4
4
8
12
16
20
-20
-16
-12
-8
-4
4
8
12
16
20
x
y

Answer 1

To complete the table of function values for the function \( f(x) = -x^2 - 8 \), we will calculate \( f(x) \) for each given \( x \).

### Function Evaluation
1. For \( x = -2 \):
\[
f(-2) = -(-2)^2 - 8 = -4 - 8 = -12
\]

2. For \( x = -1 \):
\[
f(-1) = -(-1)^2 - 8 = -1 - 8 = -9
\]

3. For \( x = 0 \):
\[
f(0) = -(0)^2 - 8 = 0 - 8 = -8
\]

4. For \( x = 1 \):
\[
f(1) = -(1)^2 - 8 = -1 - 8 = -9
\]

5. For \( x = 2 \):
\[
f(2) = -(2)^2 - 8 = -4 - 8 = -12
\]

### Completed Table
Now we can fill in the values in the table:

| \( x \) | \( f(x) \) |
|-----------|---------------|
| -2 | -12 |
| -1 | -9 |
| 0 | -8 |
| 1 | -9 |
| 2 | -12 |

### Graphing the Function
To graph the function \( f(x) = -x^2 - 8 \):

1. The function is a downward-opening parabola because the coefficient of \( x^2 \) is negative.
2. The vertex of the parabola is located at the point on the y-axis where it achieves its maximum value, which is at \( y = -8 \) when \( x = 0 \).
3. The function decreases as you move away from the vertex.

### Points to Plot
You may plot the calculated points:
- \( (-2, -12) \)
- \( (-1, -9) \)
- \( (0, -8) \)
- \( (1, -9) \)
- \( (2, -12) \)

### Drawing the Graph
1. Draw a horizontal axis (x-axis) and a vertical axis (y-axis).
2. Mark the points found above on the graph.
3. Draw a smooth curved line connecting the points to represent the parabola.

To visualize the graph accurately, ensure that the coordinates align properly, and the parabola opens downward as described.

If you have a graphing tool, you can input \( f(x) = -x^2 - 8 \) directly to see the entire parabola.