1. **State the problem:** We need to sketch the graph of the relation given by the equation $$y = -(x - 2)(x + 3)$$. 2. **Understand the equation:** This is a quadratic function in factored form. The general form is $$y = a(x - r_1)(x - r_2)$$ where $r_1$ and $r_2$ are the roots (x-intercepts) and $a$ determines the direction and width of the parabola. 3. **Find the roots:** Set $$y = 0$$ to find the x-intercepts. $$0 = -(x - 2)(x + 3)$$ This implies either: $$x - 2 = 0 \Rightarrow x = 2$$ or $$x + 3 = 0 \Rightarrow x = -3$$ So the roots are $x = 2$ and $x = -3$. 4. **Determine the direction of the parabola:** The coefficient in front is $-1$, which is negative, so the parabola opens downward. 5. **Find the vertex:** The vertex lies midway between the roots. $$x_{vertex} = \frac{2 + (-3)}{2} = \frac{-1}{2} = -0.5$$ Substitute $x = -0.5$ into the equation to find $y$: $$y = -((-0.5) - 2)((-0.5) + 3) = -(-2.5)(2.5) = -(-6.25) = 6.25$$ So the vertex is at $$(-0.5, 6.25)$$. 6. **Summary:** - Roots (x-intercepts): $-3$ and $2$ - Vertex: $(-0.5, 6.25)$ - Opens downward This information is enough to sketch the parabola. **Final answer:** The graph is a downward-opening parabola with roots at $x = -3$ and $x = 2$, and vertex at $(-0.5, 6.25)$.