1. **State the problem:** We need to sketch the graph of the function $$y = |x + 3a|$$ where $$a$$ is a positive constant. 2. **Understand the function:** The function is an absolute value function, which generally has a V-shaped graph. 3. **Vertex location:** The expression inside the absolute value is $$x + 3a$$. The vertex occurs where the inside expression equals zero: $$x + 3a = 0 \implies x = -3a$$ So, the vertex is at $$(-3a, 0)$$. 4. **Shape and direction:** The absolute value function opens upwards, so the graph forms a V shape with the vertex at $$(-3a, 0)$$. 5. **Arms of the graph:** For $$x > -3a$$, $$y = x + 3a$$ (a line with slope 1). For $$x < -3a$$, $$y = -(x + 3a) = -x - 3a$$ (a line with slope -1). 6. **Summary:** The graph is a V-shaped absolute value function with vertex at $$(-3a, 0)$$ and arms extending upward symmetrically with slopes 1 and -1. Final answer: The graph of $$y = |x + 3a|$$ is a V-shaped graph with vertex at $$(-3a, 0)$$ and arms opening upwards.