Final answer:
The vertex of the parabola is (-3, -11), the focus is (-3, -10.75), and the axis of symmetry is x = -3.
Step-by-step explanation:
The given equation is in the form y = -x^2 - 6x - 14. To identify the vertex, focus, and axis of symmetry, we can rewrite the equation in vertex form, which is y = a(x - h)^2 + k. Comparing this form to the given equation, we can see that a = -1, h = -3, and k = -11. The vertex of the parabola is (h, k), so the vertex is (-3, -11).
The formula for finding the focus of a parabola in vertex form is (h, k + 1/(4a)). Plugging in the values, we get (-3, -11 + 1/(-4)). Simplifying, the focus is (-3, -10.75).
The axis of symmetry of a parabola is a vertical line that passes through the vertex. So, the axis of symmetry for this parabola is the line x = h, which in this case is x = -3.