1. **State the problem:** We are given the quadratic function $y = -x^2 - 2x + 4$ and need to find the vertex, axis of symmetry, direction the parabola opens, domain, and range. 2. **Formula for vertex:** The vertex of a parabola $y = ax^2 + bx + c$ is at $x = -\frac{b}{2a}$. 3. **Calculate the vertex's x-coordinate:** Here, $a = -1$, $b = -2$, so $$x = -\frac{-2}{2 \times -1} = -\frac{-2}{-2} = -1.$$ 4. **Calculate the vertex's y-coordinate:** Substitute $x = -1$ into the function: $$y = -(-1)^2 - 2(-1) + 4 = -1 + 2 + 4 = 5.$$ 5. **Vertex:** The vertex is at $(-1, 5)$. 6. **Axis of symmetry:** The axis of symmetry is the vertical line through the vertex's x-coordinate: $$x = -1.$$ 7. **Direction parabola opens:** Since $a = -1 < 0$, the parabola opens downward. 8. **Domain:** The domain of any quadratic function is all real numbers: $$(-\infty, \infty).$$ 9. **Range:** Because the parabola opens downward and the vertex is the maximum point at $y=5$, the range is: $$(-\infty, 5].$$