Final answer:
The vertex is (-4, -5), the axis of symmetry is x = -4, and the function has a maximum. The domain of the function is all real numbers, and the range is {y ≤ -5}.
Step-by-step explanation:
The given function is f(x) = - (x+4)^2 - 5. To identify the vertex, axis of symmetry, minimum or maximum, domain, and range, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. Comparing the given function to the vertex form, we can see that a = -1, h = -4, and k = -5. The vertex is therefore (-4, -5), the axis of symmetry is x = -4, and since the coefficient of a is negative, the function has a maximum. The domain of the function is all real numbers, and the range is {y ≤ -5}.