Final answer:
The vertex of the function y=-(x+3)² -6 is (-3, -6).
Step-by-step explanation:
A vertex of a quadratic function is the point where the parabola representing the function reaches its maximum or minimum value.
The x-coordinate of the vertex can be found using the formula -b / (2a), and the y-coordinate can be found by substituting the x-coordinate into the equation.
The given equation is y=-(x+3)² -6.
In this form, the equation represents a quadratic function in vertex form, y = a(x-h)² + k, where (h,k) represents the vertex of the parabola.
Comparing the given equation with the vertex form, we can see that h = -3 and k = -6.
Therefore, the vertex of the function is (-3, -6). In this case, the vertex is the point in the graph where the function reaches its minimum value.