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# Lesson Worksheet: Two-Variable Quadratic Inequalities Mathematics

In this worksheet, we will practice representing solutions to quadratic inequalities in two variables graphically.

**Q1: **

Write the inequality that represents the shaded area of the following graph.

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**Q2: **

Which of the following is the graph of the inequality ?

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**Q3: **

Graph the equation and, using this graph, shade the solution of the inequality .

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**Q4: **

You are a member of a theater production crew. You use manila rope to support lighting, scaffolding, and other equipment. The weight (in pounds) that can be safely supported by a rope with diameter (in inches) is given by .

Using the graph of the inequality, can 1,000 pounds of theater equipment be supported by a rope where ?

- ANo
- BYes

**Q5: **

In 1992, the average income (in thousands of dollars) for a teacher aged years could be modeled by .

Graph the equation for average income versus age for teachers aged 20 and over.

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On the same graph draw a line which represents an average income of $25,000.

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Using the last graph, find for what ages the average income for a teacher exceeded 25 thousand dollars.

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**Q6: **

Write the inequality that represents the shaded area of the following graph.

- A
- B
- C
- D
- E

**Q7: **

Which of the following is the graph of the inequality ?

- A
- B
- C
- D
- E

**Q8: **

Write the inequality that represents the shaded area of the following graph.

- A
- B
- C
- D
- E

**Q9: **

Write the inequality that represents the shaded area of the following graph.

- A
- B
- C
- D
- E