1. Choose some values for x. For simplicity, let's choose x = -3, -2, -1, 0, 1, and 2. These values will help us determine the corresponding y-values.
2. Substitute each value of x into the equation Y = |x + 1| - 2 to find the corresponding y-values.
- For x = -3: Y = |-3 + 1| - 2 = |-2| - 2 = 2 - 2 = 0
- For x = -2: Y = |-2 + 1| - 2 = |-1| - 2 = 1 - 2 = -1
- For x = -1: Y = |-1 + 1| - 2 = |0| - 2 = 0 - 2 = -2
- For x = 0: Y = |0 + 1| - 2 = |1| - 2 = 1 - 2 = -1
- For x = 1: Y = |1 + 1| - 2 = |2| - 2 = 2 - 2 = 0
- For x = 2: Y = |2 + 1| - 2 = |3| - 2 = 3 - 2 = 1
3. Plot the points on a coordinate plane. The x-values will be plotted on the x-axis, and the corresponding y-values will be plotted on the y-axis.
- (-3, 0)
- (-2, -1)
- (-1, -2)
- (0, -1)
- (1, 0)
- (2, 1)
4. Connect the points with a smooth curve. Since the equation involves absolute value, the graph will have a "V" shape with the vertex at (-1, -2).
The resulting graph will have a "V" shape with the vertex at (-1, -2), and it will pass through the points (-3, 0), (-2, -1), (0, -1), (1, 0), and (2, 1).