1. The problem is to find the coordinates of the vertex of the parabola given by the function $$y = (x + 3)^2 + 4$$. 2. Recall that the vertex form of a parabola is $$y = a(x - h)^2 + k$$, where $$(h, k)$$ is the vertex. 3. In the given function, $$y = (x + 3)^2 + 4$$, we can rewrite $$x + 3$$ as $$x - (-3)$$, so $$h = -3$$ and $$k = 4$$. 4. Therefore, the vertex of the parabola is at the point $$(-3, 4)$$. 5. This vertex represents the minimum point of the parabola since the coefficient of the squared term is positive (1). Final answer: The vertex coordinates are $$\boxed{(-3, 4)}$$.