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Muh Ikhwan

Muh Ikhwan. SMA Negeri 3 Semarang. QUADRATIC INEQUALITIES. By : Muh Ikhwan SMA Negeri 3 Semarang. Standard Competition. Using the characteristics and laws of quadratic Inequalities. Indicator. Determining the solution set of quadratic inequalities by the graph

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Muh Ikhwan

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  1. Muh Ikhwan SMA Negeri 3 Semarang

  2. QUADRATIC INEQUALITIES By : Muh Ikhwan SMA Negeri 3 Semarang

  3. Standard Competition • Using the characteristics and laws of quadratic Inequalities

  4. Indicator • Determining the solution set of quadratic inequalities by the graph • Determining the solution set of quadratic inequalities by number line

  5. Learning Prerequisites: Students will be able to solve the quadratic inequalities by graphical and number line method. Aims and Objectives: Sketching the graph of the corresponding quadratic expressions. Method of factorization.

  6. QUADRATIC INEQUALITIES Concept and Exercises (Exploration, Elaboration and Confirmation ) Quiz Interactive Download : http://ikhwansmaga.wordpress.com/

  7. Method ofGraph sketching

  8. Example 1: Solve the quadratic inequality x2 – 5x + 6 > 0 graphically.

  9. Procedures: Step (1): The corresponding quadratic function is y = x2 – 5x + 6 Step (2): Factorize x2 – 5x + 6 we have y = (x – 2)(x – 3) ,i.e. y = 0, when x = 2 or x = 3 Step (3): Sketch the graph of y = x2 – 5x + 6 Step (4): Find the solution from the graph

  10. y y = (x – 2)(x – 3) , y = 0, when x = 2 or x = 3.  x 0 2 3 Sketch the graph y =x2 – 5x + 6 . What is the solution of x2 – 5x + 6 > 0 ?

  11. so we choose the portion above the x-axis. 2 3 We need to solve x 2 – 5x + 6 > 0, y The portion of the graph above the x-axis represents y > 0 (i.e. x 2 – 5x + 6 > 0) x 0 The portion of the graph below the x-axis represents y < 0 (i.e. x 2 – 5x + 6 < 0)

  12. 2 3 y When x < 2, the curve is above the x-axis i.e., y > 0 x2 – 5x + 6 > 0 When x > 3, the curve is above the x-axis i.e., y > 0 x2 – 5x + 6 > 0 x 0

  13. or From the sketch, we obtain the solution

  14. By Number Line ?

  15. or 2 0 3 Number Line Solution:

  16. Example 2: Solve the quadratic inequality x2 – 5x + 6 < 0. Same method as example 1 !!!

  17. 2 3 y x2 – 5x + 6 < 0 x 0 When 2 < x < 3, the curve is below the x-axis i.e., y < 0 x2 – 5x + 6 < 0

  18. From the sketch, we obtain the solution 2 < x < 3

  19. 2 0 3 Number Line Solution: 2 < x < 3

  20. Solve Exercise 1: y x 0 1 –2 –2 0 1 Find the x-intercepts of the curve: (x + 2)(x – 1)=0 x = –2 or x = 1 Answer: x < –2 or x > 1

  21. Solve Exercise 2: y x 0 4 –3 –3 0 4 Find the x-intercepts of the curve: x2 – x – 12 = 0 (x + 3)(x – 4)=0 x = –3 or x = 4 Answer: –3 < x < 4

  22. y x 0 5 –7 0 –7 5 Find the x-intercepts of the curve: (x + 7)(x – 5)=0 x = –7 or x = 5 Exercise 3: Solve Solution: –7 < x < 5

  23. y x 0 2 3 –3 0 –3 2 3 Find the x-intercepts of the curve: (x + 3)(3x – 2)=0 x = –3 or x = 2/3 Exercise 4: Solve Solution: x –3 or x 2/3

  24. Quiz interactive on line http://www.classzone.com/etest/viewTestPractice.htm?testId=4293&seqNumber=4&testSessionId=null&startUrl=http://www.classzone.com/books/algebra_1/lessonquiz_national.cfm

  25. THANK YOU

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