1. The problem asks to identify which inequality corresponds to a graph of a downward-opening parabola with x-intercepts near $x=2$ and $x=4$, vertex near $(3,5)$, and shading below the parabola. 2. The general form of a quadratic inequality is $y \lessgtr a(x-r_1)(x-r_2)$ where $r_1$ and $r_2$ are the roots (x-intercepts), and $a$ determines the parabola's opening direction and width. 3. Since the parabola opens downward, $a$ must be negative. 4. The x-intercepts are approximately $2$ and $4$, so the factors are $(x-2)$ and $(x-4)$. 5. The vertex near $(3,5)$ is consistent with the parabola $y = -5(x-2)(x-4)$ because the vertex of $y = a(x-r_1)(x-r_2)$ is at $x = \frac{r_1 + r_2}{2} = 3$. 6. The inequality shading below the parabola means $y < -5(x-2)(x-4)$. 7. Therefore, the inequality shown is: $$y < -5(x-2)(x-4)$$