Quadratic Inequality Dd93F8

1. **State the problem:** We need to identify the graph that represents the quadratic inequality $$y \geq x^2 - 6x + 11$$. 2. **Rewrite the quadratic expression:** The quadratic can be rewritten by completing the square: $$x^2 - 6x + 11 = (x^2 - 6x + 9) + 2 = (x - 3)^2 + 2$$ 3. **Interpret the inequality:** The inequality $$y \geq (x - 3)^2 + 2$$ means the graph is a parabola opening upwards with vertex at $$(3, 2)$$. 4. **Graph features:** - The parabola opens upward because the coefficient of $$x^2$$ is positive. - The vertex is at $$(3, 2)$$. - The region on and above the parabola is shaded because of the $$\geq$$ sign. 5. **Summary:** The correct graph will show an upward-opening parabola shifted right by 3 and up by 2, with the area on and above the parabola shaded.