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Graph the function y=-2|x|-4 using the given table of values shown in the image

The image you've provided shows a table of values, likely being used to plot the graph of the function \( y = -2|x| - 4 \). Unfortunately, the quality of the image makes it difficult to extract the exact values from the table. However, I can guide you on how to create a table of values and plot the graph based on the given function.

### Steps to Graph \( y = -2|x| - 4 \):

1. **Understand the function**:
   - The function \( y = -2|x| - 4 \) is an absolute value function that has been reflected vertically (because of the negative sign in front of the absolute value) and shifted down by 4 units.
   
2. **Create a table of values**:
   - Choose a set of values for \( x \) (typically around the vertex, including negative, zero, and positive values).
   - Calculate \( y \) for each \( x \) value using the function.

### Example Table of Values:

| \( x \) | \( y = -2|x| - 4 \) |
|:------:|:-------------------:|
|  -3    |  -2(3) - 4 = -10    |
|  -2    |  -2(2) - 4 = -8     |
|  -1    |  -2(1) - 4 = -6     |
|   0    |  -2(0) - 4 = -4     |
|   1    |  -2(1) - 4 = -6     |
|   2    |  -2(2) - 4 = -8     |
|   3    |  -2(3) - 4 = -10    |

3. **Plot these points** on a coordinate plane:
   - For each pair \((x, y)\), plot the corresponding point.
   - Connect the points with straight lines, forming a "V" shape.

4. **Analyze the graph**:
   - The vertex of the graph is at the point \( (0, -4) \).
   - The graph opens downward due to the negative coefficient of the absolute value.
   - The slope is steep because of the factor of 2, meaning for every unit change in \( x \), \( y \) changes by 2 units.

### Sketching the Graph:

The graph will be a downward-pointing V-shape with the vertex at \( (0, -4) \). The line segments extend left and right with a slope of -2, reflecting across the y-axis.

Would you like further details or have any questions about this process?

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### Relative Questions:

1. How does the coefficient in front of the absolute value affect the steepness of the graph?
2. What does the negative sign before the absolute value function indicate about the graph's direction?
3. How would the graph of \( y = -2|x| - 4 \) differ from \( y = 2|x| + 4 \)?
4. How do you determine the vertex of an absolute value function?
5. What would happen to the graph if we changed the function to \( y = -2|x + 1| - 4 \)?

### Tip:
Remember that the absolute value function creates a V-shaped graph, with the vertex indicating the lowest or highest point depending on the sign of the coefficient in front of the absolute value.

Learn how to graph the function y=-2|x|-4 using a table of values approach. This guide includes step-by-step instructions on creating a table of values, plotting the graph, and understanding key graph characteristics. Suitable for high school students studying absolute value functions and graphing techniques.

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