1. **State the problem:** We are given a quadratic function in factored form $$f(x) = a(x - h)(x - k)$$ with $$h < k$$ and a graph showing points where the function crosses the x-axis at $$x = h$$ and $$x = k$$, and a point on the graph at $$(0, -8)$$. 2. **Find the values of $$h$$ and $$k$$:** From the graph, the roots (x-intercepts) are where $$f(x) = 0$$. These occur at $$x = h$$ and $$x = k$$. From the graph, these intercepts are at $$x = -1$$ and $$x = 2$$. Since $$h < k$$, we have: $$h = -1, \quad k = 2$$ 3. **Find the value of $$a$$:** Use the point given on the graph, which is $$f(0) = -8$$. Substitute $$x = 0$$, $$h = -1$$, and $$k = 2$$ into the function: $$f(0) = a(0 - (-1))(0 - 2) = a(1)(-2) = -2a$$ Set equal to $$-8$$: $$-2a = -8$$ Divide both sides by $$-2$$: $$\cancel{-2}a = \cancel{-2}4$$ $$a = 4$$ 4. **Determine the equation of the axis of symmetry:** The axis of symmetry for a quadratic in factored form $$a(x - h)(x - k)$$ is the vertical line halfway between $$h$$ and $$k$$: $$x = \frac{h + k}{2}$$ Substitute $$h = -1$$ and $$k = 2$$: $$x = \frac{-1 + 2}{2} = \frac{1}{2} = 0.5$$ **Final answers:** - $$h = -1$$ - $$k = 2$$ - $$a = 4$$ - Axis of symmetry: $$x = 0.5$$