solving-quadratic-inequalities-240102152639-aae00a95.pptx

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1. GOOD MORNING GRADE 9

2. Mini-Activity: “Equation or Inequality?”

6. GREATER THAN LESS THAN EQUAL

7. ≥

8. ≤

9. >

10. <

11. =

12. Inequality Scenarios

13. WHO IS WHO?

14. QUADRATIC INEQUALITIES A Quadratic Inequality is an inequality that contains a polynomial of degree 2.

15. SOLVING QUADRATIC INEQUALITY Grade 9

16. 1. Illustrate quadratic inequalities 2. Solve quadratic inequalities. 3. Relate quadratic inequalities to real life situation. OBJECTIVES:

17. Activity 2: Equation or Not? Statement Quadratic Inequality? (Yes/No) Reason 1. +3x-4 >0     x+2=     3. 2 x+5 >0     4.     5.     6. >0     7. x+1 ≥0     8. 7y-5 <12     9. + =     10. -16 ≥0     11. +4p+3 <0     12. q+7 >10     13. -5r+2 ≤0     14. + -1 >0     15. +1=0   Statement Quadratic Inequality? (Yes/No) Reason         3. 2 x+5 >0                     8. 7y-5 <12                 12. q+7 >10              

18. STEPS IN SOLVING QUADRATIC INEQUALITIES Express the quadratic inequality as a quadratic equation in the form of factoring and then solve for x. Locate the numbers found in step 1 on a number line. The number line will be divided into three regions. Choose a test point each region and substitute the test point to the original inequality. If its hold true, then the region belongs to the solution set, otherwise, it is not part of the solution set.

19. How to solve Quadratic Inequalities?

20. EXAMPLE 1.   ( x + 2) (x + 5) = 0 ( x + 2) =0 and(x + 5) = 0 X = -2 and x = -5 b. Express the quadratic inequality as a quadratic equation in the form of factoring and then solve for x. Locate the numbers found in step 1 on a number line. The number line will be divided into three regions. Choose a test point each region and substitute the test point to the original inequality. If its hold true, then the region belongs to the solution set, otherwise, it is not part of the solution set.

21. EXAMPLE 1. c. Let x = -7 49 – 49 + 10 0 10 0 ( True) Let x = -3 Let x = 0 ( ) Express the quadratic inequality as a quadratic equation in the form of and then solve for x. Locate the numbers found in step 1 on a number line. The number line will be divided into three regions. Choose a test point each region and substitute the test point to the original inequality. If its hold true, then the region belongs to the solution set, otherwise, it is not part of the solution set.

22. EXAMPLE 1. Therefore, the inequality is true for any value of x in the interval and these intervals exclude -2 and -5. The solution set is

23. EXAMPLE 1. Therefore, the inequality is true for any value of x in the interval and these intervals exclude -2 and -5. The solution set is

24. QUADRATIC INEQUALITY A Quadratic Inequality is an equality that contains a polynomial of degree 2.