Quadratic Inequality Points B2E40D

1. **State the problem:** We need to determine which points satisfy the inequality $$y \geq x^2 - 2x - 15$$. 2. **Recall the inequality:** For each point $(x,y)$, substitute $x$ and $y$ into the inequality and check if it holds true. 3. **Check each point:** - For $(-4, 2)$: $$x^2 - 2x - 15 = (-4)^2 - 2(-4) - 15 = 16 + 8 - 15 = 9$$ Check if $2 \geq 9$? No. - For $(0, 0)$: $$x^2 - 2x - 15 = 0^2 - 2(0) - 15 = -15$$ Check if $0 \geq -15$? Yes. - For $(2, 6)$: $$x^2 - 2x - 15 = 2^2 - 2(2) - 15 = 4 - 4 - 15 = -15$$ Check if $6 \geq -15$? Yes. - For $(1, -6)$: $$x^2 - 2x - 15 = 1^2 - 2(1) - 15 = 1 - 2 - 15 = -16$$ Check if $-6 \geq -16$? Yes. 4. **Conclusion:** Points $(0,0)$, $(2,6)$, and $(1,-6)$ satisfy the inequality. **Final answer:** The points that satisfy $y \geq x^2 - 2x - 15$ are $(0,0)$, $(2,6)$, and $(1,-6)$. Therefore, the correct choices are b), c), and d).