1. **State the problem:** We need to graph the absolute value function $$y = 6|x + 4| - 2$$ and identify its key features. 2. **Formula and rules:** The general form of an absolute value function is $$y = a|x - h| + k$$ where $ (h, k) $ is the vertex. 3. **Find the vertex:** Rewrite the function as $$y = 6|x - (-4)| - 2$$ so the vertex is at $(-4, -2)$. 4. **Plot the vertex:** This is the point where the graph changes direction. 5. **Determine the slope:** For $x > -4$, the function behaves like $$y = 6(x + 4) - 2$$ which has slope 6. For $x < -4$, the function behaves like $$y = 6(-(x + 4)) - 2 = -6x - 24 - 2 = -6x - 26$$ which has slope -6. 6. **Plot additional points:** - At $x = -3$, $$y = 6|-3 + 4| - 2 = 6(1) - 2 = 4$$ - At $x = -5$, $$y = 6|-5 + 4| - 2 = 6(1) - 2 = 4$$ 7. **Draw the V-shaped graph:** Connect the points with lines of slopes 6 and -6 meeting at the vertex. **Final answer:** The vertex is at $(-4, -2)$, the graph opens upwards with slopes 6 and -6 on either side of the vertex.