1. **State the problem:** Find the left and right x-intercepts, the axis of symmetry, and the vertex of the quadratic function $$y = -(x + 1)(x - 5)$$. 2. **Find the x-intercepts:** The x-intercepts occur where $$y=0$$. Set $$-(x + 1)(x - 5) = 0$$. This implies $$(x + 1)(x - 5) = 0$$. So, $$x + 1 = 0$$ or $$x - 5 = 0$$. Therefore, $$x = -1$$ or $$x = 5$$. The left x-intercept is $$(-1, 0)$$ and the right x-intercept is $$(5, 0)$$. 3. **Find the axis of symmetry:** The axis of symmetry is the vertical line that passes through the midpoint of the x-intercepts. Calculate the midpoint: $$x = \frac{-1 + 5}{2} = \frac{4}{2} = 2$$. So, the axis of symmetry is $$x = 2$$. 4. **Find the vertex:** The vertex lies on the axis of symmetry. Substitute $$x=2$$ into the original equation: $$y = -(2 + 1)(2 - 5) = -(3)(-3) = 9$$. So, the vertex is $$(2, 9)$$. **Final answers:** - Left x-intercept: $$(-1, 0)$$ - Right x-intercept: $$(5, 0)$$ - Axis of symmetry: $$x = 2$$ - Vertex: $$(2, 9)$$