1. **State the problem:** Graph the equation $y = |x - 2| - 4$. 2. **Recall the absolute value function:** The graph of $y = |x|$ is a V-shaped graph with vertex at the origin $(0,0)$. 3. **Transformations:** For $y = |x - 2| - 4$, the graph shifts right by 2 units and down by 4 units. 4. **Vertex:** The vertex is at $(2, -4)$. 5. **Plot points:** Choose values around the vertex: - At $x=2$, $y=|2-2|-4=0-4=-4$ (vertex). - At $x=1$, $y=|1-2|-4=1-4=-3$. - At $x=3$, $y=|3-2|-4=1-4=-3$. 6. **Shape:** The graph forms a V with vertex at $(2,-4)$ opening upwards. **Final answer:** The graph of $y = |x - 2| - 4$ is a V-shaped graph with vertex at $(2, -4)$ opening upwards.