Illustrations of Quadratic Equations.pptx

Illustrations of Quadratic Equations

1. Illustrations of Quadratic Equations : Math 9

2. Learning Competency: Objectives: 1. Illustrate quadratic equation. 2. Write quadratic equation in the form 𝑎 + 𝑏𝑥 + 𝑐 = 0. 3. Identify the numerical values of a, b and c. 4. Show critical thinking skills in identifying and illustrating quadratic equations   illustrate quadratic equations M9AL-1a- 1

3. PRETEST: 1. In 3𝑥² − 𝑥 + 5 = 0, what is the quadratic term? 3x 3x² x² –x

4. PRETEST: 2. What is the numerical value of b in 3 𝑥² − 𝑥 + 5 = 0 ? -1 1 3 5

5. PRETEST: 3 .How is (𝑥 − 7)(𝑥 + 7) = 0 written in the form a𝑥² + bx + c = 0? a. 2𝑥² − 14 = 0 b. 𝑥² + 49 = 0 c. 𝑥² − 49 = 0 d. 𝑥² = 49

6. PRETEST: 4. In the equation 2𝑥² = 10, what is the value of b ? 2 10 −10

7. PRETEST: 5 .Which of the following is not a quadratic equation? 2𝑥 − 𝑥² = 3𝑥² (𝑥 + 5)² = 𝑥² c. 𝑥 (2𝑥 − 7) = 1 d. (𝑥 − 1)(2𝑥 + 3) = 0

8. PRETEST:

9. Explore:

10. EXPLORE: WHAT ARE THE REPRESENTATION OF THESE PARABOLIC CURVES?

11. RECAll : What do you call to the given expression? What is the type of this polynomial? Why is it a trinomial?

12. RECAP: What do you notice to the highest exponent of x?

13. RECAP: Classify the polynomials.

14. RECAll :

15. RECAll : Questions: a. How did you find each product? b. In finding each product, what mathematics concepts or principles did you apply? Explain how you applied these mathematics or principles. c.How would you describe the products obtained? Are the products polynomials? If YES, what common characteristics do these polynomials have?

16. LESSON PROPER: What do you notice to the highest exponent of x? What do you call of this equation?

17. LESSON PROPER: How do you define quadratic equation? What do you call to each term of the equation?

18. LESSON PROPER: The name quadratic comes from quad meaning squares, because a quadratic equation is a polynomial equation where the variable is of the second degree . It is written in the form 𝑎𝑥²+𝑏𝑥 +𝑐=0, where a, b and c are real numbers and a ≠ 0 .

19. LESSON PROPER: What if a = 0 ? If a = 0 , ( ) 𝑥²+𝑏𝑥 +𝑐=0 𝑏𝑥 +𝑐=0 Why is it a linear equation ?

20. ACTIVITY: Quadratic Not Quadratic Quadratic Quadratic Not Quadratic Not Quadratic

21. LESSON PROPER: What made these equations quadratic ? 3𝑥² = 9 3𝑥²- 9 = 0 a=3, b= 0, c = -9 Are these quadratic equations written in standard form ?

22. LESSON PROPER: a = 2 2𝑥² - 3 = 6x b= -6 2𝑥² - 6x -3 = 0 c= -3

23. LESSON PROPER: How can we expand these equations ? Are these equations quadratic ?

24. LESSON PROPER: How can we expand this equation ? Let us expand this equation. 3x(x) – 3x(2) = 10 3𝑥² – 6x = 10 3𝑥² – 6x – 10 = 0

25. LESSON PROPER: How can we expand this equation ? 2x(x) – 2x(1)+5(x)- 5 (1) = -6 2𝑥²–2x+5x – 5+6 = 0 2𝑥² + 3x + 1 = 0

26. LET’S PRACTICE: How can we expand th e se equations ? 2x(x) – 2x(1)+5(x)- 5 (1) = -6 2𝑥²–2x+5x – 5+6 = 0 2𝑥² + 3x + 1 = 0

27. LET US Analyze: Who got the correct answer ? 2x(x) – 2x(1)+5(x)- 5 (1) = -6 2𝑥²–2x+5x – 5+6 = 0 2𝑥² + 3x + 1 = 0

28. LET US SUMMARIZE: What is quadratic equation ? How can we rewrite/transform the quadratic equations in a standard form ?

29. Evaluation:

30. Assignment