1. **State the problem:** Find the vertex of the parabola given by the function $$f(x) = -x^2 - 12x - 34$$. 2. **Recall the vertex formula:** For a quadratic function $$f(x) = ax^2 + bx + c$$, the vertex $(h, k)$ is found using: $$h = -\frac{b}{2a}$$ $$k = f(h)$$ 3. **Identify coefficients:** Here, $$a = -1$$, $$b = -12$$, and $$c = -34$$. 4. **Calculate the x-coordinate of the vertex:** $$h = -\frac{-12}{2 \times -1} = -\frac{-12}{-2} = -6$$ 5. **Calculate the y-coordinate of the vertex by substituting $$h$$ into $$f(x)$$:** $$k = f(-6) = -(-6)^2 - 12(-6) - 34 = -36 + 72 - 34$$ $$k = 2$$ 6. **Write the vertex coordinates:** The vertex is at $$(-6, 2)$$. **Final answer:** $$\boxed{(-6, 2)}$$