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The image you have provided contains a table for filling in the missing information about quadratic inequalities, specifically for the case where the inequality symbol is "≥", indicating a quadratic inequality in the form \( ax^2 + bx + c \geq 0 \).

Here is a breakdown of the missing entries based on the given information:

1. **Inequality Symbol**: \( \geq \)
2. **Leading Coefficient**: \( a > 0 \) (This means the parabola opens upwards).
3. **The direction in which the parabola opens**: **Upwards**.
4. **x-values from the graph included in the solution**: **Above the x-axis** (since we are considering where the graph is greater than or equal to zero, meaning the part of the parabola that is on or above the x-axis).
5. **Roots**: **Included** (since we have "greater than or equal to", the roots are part of the solution).
6. **Solution Set**: \( \{x | x \leq x_1 \text{ or } x \geq x_2\} \) (This represents the intervals where the parabola is above or on the x-axis).

Would you like more details or any clarifications on this topic?

Here are 5 related questions to expand on this:
1. What is the difference between \( \geq \) and \( > \) in terms of solution sets for quadratic inequalities?
2. How do we calculate the roots of a quadratic inequality?
3. Why does the parabola open upwards when \( a > 0 \)?
4. How would the solution change if the inequality were \( \leq \)?
5. What happens to the solution set if the quadratic has no real roots?

**Tip**: When solving quadratic inequalities, always sketch the parabola to visually confirm where the graph is above or below the x-axis for a clearer understanding of the solution set.

Fill in the missing information about quadratic inequalities where the inequality symbol is '≥'.

Understand how to solve quadratic inequalities with the '≥' symbol. Learn the solution set when a parabola opens upwards (a > 0), including roots and intervals where the graph is above the x-axis. Suitable for students in Grades 9-11.

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