Shade Inequality Ad3800

1. **State the problem:** We need to shade the region where the inequality $y \leq x^2 - x - 20$ holds true and label this region as $R$. 2. **Understand the inequality:** The inequality $y \leq x^2 - x - 20$ means we want all points $(x,y)$ where the $y$-value is less than or equal to the value of the quadratic function $x^2 - x - 20$. 3. **Graph the boundary:** The boundary is the parabola given by the equation $$y = x^2 - x - 20.$$ This parabola opens upwards because the coefficient of $x^2$ is positive. 4. **Determine the region to shade:** Since the inequality is $y \leq x^2 - x - 20$, we shade the region below or on the parabola. 5. **Label the region:** The shaded region below the parabola is labeled $R$. **Final answer:** The region $R$ is the set of points $(x,y)$ such that $y \leq x^2 - x - 20$, which is the area on or below the parabola $y = x^2 - x - 20$.