1. **State the problem:** We are given the function $$y = (x+3)^2 + 2$$ and need to find the function's vertex and describe its graph. 2. **Identify the function type:** This is a quadratic function in vertex form $$y = (x-h)^2 + k$$ where the vertex is at $$(h, k)$$. 3. **Find the vertex:** Here, $$h = -3$$ and $$k = 2$$, so the vertex is $$(-3, 2)$$. 4. **Describe the graph:** Since the coefficient of the squared term is positive (1), the parabola opens upwards. 5. **Summary:** - Function: $$y = (x+3)^2 + 2$$ - Vertex: $$(-3, 2)$$ - Graph: Parabola opening upwards with vertex at $$(-3, 2)$$.