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1. Quadratic Inequalities 2 nd Quarter 9TH GRADE

2. Learning Objectives At the end of this unit, you should be able to: identify quadratic inequalities; 01 solve problems involving quadratic inequalities 03 solve quadratic inequalities; and 02 9TH GRADE

3. What is a Quadratic Inequality? 9TH GRADE

4. A quadratic inequality (in one variable) is an inequality with one unknown (usually ) of degree 2. Simply put, it is like a quadratic equation but the equal sign is replaced by a less than, greater than, at most, or at least symbol. 9TH GRADE

5. It can be written in the following forms:   9TH GRADE where and are real numbers, and a ≠ 0      

6. Quadratic vs Linear Inequality 9TH GRADE

7. If the simplified form of an inequality doesn’t have 2 as the highest power of the variable x, it is not a quadratic inequality. Things to remember about quadratic inequalities: When simplified, quadratic inequalities retain 2 as the highest power of the variable x. 9TH GRADE The difference between a quadratic equation and a quadratic inequality is that the equation is equal to some number while inequality is either less than or greater than some number.

8. Critical Values, Test Intervals, and Test Numbers 9TH GRADE

9. Insert your multimedia content here Watch the Video 9TH GRADE

10. Solving Quadratic Inequalities 9TH GRADE

11. Solve the quadratic inequality   Step 1: Write one side of the inequality in the form and the other side zero.  

12. Step 2: Treat the inequality as a quadratic equation. Solve the equation. The solutions are the critical numbers of the inequality.  

13. Step 3: Use the critical numbers to determine the test intervals. The test intervals are ,  

14. Step 4: Choose one test number in each test interval and evaluate the inequality at that value. You may use the original inequality or factored form of the inequality when evaluating. Original Inequality: Factored Inequality:  

15. S t ep 4: Test Interval Test Number Evaluation Conclusion True False True Test Interval Test Number Evaluation Conclusion True False True 9TH GRADE

16. Thanks! 9TH GRADE