1. The problem is to find the vertex of the quadratic function $$x^2 + 4x + 4$$. 2. The vertex form of a quadratic function is $$y = a(x-h)^2 + k$$, where $$(h,k)$$ is the vertex. 3. To find the vertex from the standard form $$ax^2 + bx + c$$, use the formula for the x-coordinate of the vertex: $$x = -\frac{b}{2a}$$. 4. Here, $$a = 1$$, $$b = 4$$, and $$c = 4$$. 5. Calculate the x-coordinate: $$x = -\frac{4}{2 \times 1} = -\frac{4}{2} = -2$$. 6. Substitute $$x = -2$$ back into the function to find the y-coordinate: $$y = (-2)^2 + 4(-2) + 4 = 4 - 8 + 4 = 0$$. 7. Therefore, the vertex is at the coordinate $$(-2, 0)$$.