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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.

1 answer

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.