1. **Problem Statement:** Shade the region defined by the inequalities: $$y \geq 0, \quad x \leq 0, \quad y \geq x^2$$ 2. **Understanding the inequalities:** - $y \geq 0$ means the region is above or on the x-axis. - $x \leq 0$ means the region is to the left of or on the y-axis. - $y \geq x^2$ means the region is above or on the parabola $y = x^2$. 3. **Key points and boundaries:** - The parabola $y = x^2$ opens upwards. - Since $x \leq 0$, we only consider the left half of the parabola. - The region must satisfy all three inequalities simultaneously. 4. **Step-by-step solution:** 1. Plot the parabola $y = x^2$. 2. Shade the area above the parabola (since $y \geq x^2$). 3. Shade the area above the x-axis (since $y \geq 0$). 4. Shade the area to the left of the y-axis (since $x \leq 0$). 5. **Intersection of these regions:** The final shaded region is the part of the plane where all three conditions hold true simultaneously: above the parabola, above the x-axis, and left of the y-axis. 6. **Final answer:** The shaded region is the set of points $(x,y)$ such that: $$x \leq 0, \quad y \geq 0, \quad y \geq x^2$$ This is the region above the parabola $y = x^2$ on the left half-plane and above the x-axis.