1. The problem asks to graph the function $$g(x) = -3(x - 5)(x + 1)$$ and identify the x-intercepts, vertex, and axis of symmetry. 2. First, find the x-intercepts by setting $$g(x) = 0$$: $$-3(x - 5)(x + 1) = 0$$ This implies either $$x - 5 = 0$$ or $$x + 1 = 0$$, so the x-intercepts are $$x = 5$$ and $$x = -1$$. 3. The axis of symmetry for a quadratic in factored form $$a(x - r)(x - s)$$ is the vertical line halfway between the roots: $$x = \frac{r + s}{2} = \frac{5 + (-1)}{2} = \frac{4}{2} = 2$$. 4. To find the vertex, substitute $$x = 2$$ into $$g(x)$$: $$g(2) = -3(2 - 5)(2 + 1) = -3(-3)(3) = -3 \times -9 = 27$$. 5. So the vertex is at $$(2, 27)$$. 6. Summarizing: - x-intercepts: $$(5, 0)$$ and $$(-1, 0)$$ - vertex: $$(2, 27)$$ - axis of symmetry: $$x = 2$$ 7. Comparing with the options given: - Graph 1: x-intercepts (-5,0) and (1,0), vertex (-2,-27), axis x=-2 - Graph 2: x-intercepts (-1,0) and (5,0), vertex (2,-27), axis x=2 - Graph 3: x-intercepts (-1,0) and (5,0), vertex (2,27), axis x=2 - Graph 4: x-intercepts (-5,0) and (1,0), vertex (-2,27), axis x=-2 The correct option is Graph 3 because it matches the x-intercepts, vertex, and axis of symmetry found. Final answer: Graph 3