To graph the equation $y = |x - 2|$, you can start with the graph of the parent function $y = |x|$ and apply the necessary transformation.

Steps to Graph $y = |x - 2|$:

1. Parent Function:
   The parent function is $y = |x|$, which is a V-shaped graph with the vertex at the origin (0, 0). The graph opens upwards, with the left side having a slope of -1 and the right side having a slope of 1.

2. Horizontal Shift:
   The equation $y = |x - 2|$ represents a horizontal shift of the parent function $y = |x|$. Specifically, the graph will be shifted 2 units to the right.

   • Vertex: The new vertex of the graph will be at (2, 0) instead of (0, 0).
   • The V-shape remains the same, with the graph still opening upwards. The slopes of the lines on either side of the vertex are unchanged.

3. Plotting the Graph:

   • Start by plotting the vertex at the point (2, 0).
   • Then, draw the lines with a slope of 1 to the right of the vertex and -1 to the left of the vertex.

Graph Description:

• The vertex of the graph is at $(2, 0)$.
• The left side of the graph decreases linearly with a slope of -1 as $x$ decreases from 2.
• The right side of the graph increases linearly with a slope of 1 as $x$ increases from 2.

Graph Representation:

If you were to plot this on a coordinate plane, it would look like this:

• The vertex at $(2, 0)$.
• The line extends downward to the left and upward to the right, creating a V-shape.

Would you like to see the graph drawn or have further details on how the transformation was applied?

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5 Related Questions:

1. How would the graph change if the equation were $y = |x + 2|$?
2. What effect does multiplying the absolute value function by a constant have on the graph?
3. How would you graph $y = |x - 2| + 3$?
4. How does the graph of $y = |x - 2|$ compare to the graph of $y = -|x - 2|$?
5. What is the vertex form of an absolute value function?

Tip: For any transformation, always identify the type of transformation (e.g., translation, reflection, dilation) and its effect on the graph’s key features like the vertex and slope.