Question

Graph the equation y equals 4 |x|. Let x equals negative 3 comma minus​2, minus​1, ​0, 1,​ 2, and 3.
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Part 1
Find the following​ y-values. Then choose the correct graph of the equation to the right.

Answer 1

To graph the equation \( y = 4|x| \), we first need to calculate the \( y \)-values for the given \( x \)-values: -3, -2, -1, 0, 1, 2, and 3.

### Calculation of y-values:

1. When \( x = -3 \):
\[
y = 4|-3| = 4 \times 3 = 12
\]

2. When \( x = -2 \):
\[
y = 4|-2| = 4 \times 2 = 8
\]

3. When \( x = -1 \):
\[
y = 4|-1| = 4 \times 1 = 4
\]

4. When \( x = 0 \):
\[
y = 4|0| = 4 \times 0 = 0
\]

5. When \( x = 1 \):
\[
y = 4|1| = 4 \times 1 = 4
\]

6. When \( x = 2 \):
\[
y = 4|2| = 4 \times 2 = 8
\]

7. When \( x = 3 \):
\[
y = 4|3| = 4 \times 3 = 12
\]

### Summary of x and y-values:
- \( (-3, 12) \)
- \( (-2, 8) \)
- \( (-1, 4) \)
- \( (0, 0) \)
- \( (1, 4) \)
- \( (2, 8) \)
- \( (3, 12) \)

### Graphing the Points:
You can plot the points as follows:
- Point A: \((-3, 12)\)
- Point B: \((-2, 8)\)
- Point C: \((-1, 4)\)
- Point D: \((0, 0)\)
- Point E: \((1, 4)\)
- Point F: \((2, 8)\)
- Point G: \((3, 12)\)

### Shape of the Graph:
The graph of \( y = 4|x| \) is a V-shaped graph that opens upward. The vertex is at the point (0,0) and it has symmetry around the y-axis.

With the calculated points, you can now sketch the graph. If you have any options for possible graphs, look for one that resembles the shape described with the calculated points.