COMPLETING THE SQUARE 2023-2024 Week 4 day 1 - Polynel Bautista.pptx

Completing the square

1. MATHEMATICS GRADE 9 canva ROSAL CAMIA

2. FIVE MINUTE HABBIT MATHEMATICS

3. Solve the following: -33+ 12 – 6 = 2,789 ÷ 13 = 5ab + 9ab – 6ab = -25x + 10x – 5x + 7x= MATHEMATICS

4. MOTIVATION MATHEMATICS

5. Express each of the following perfect square trinomial as a square of binomial: x² + 6x + 9 x² -14x + 49 x² + 2x + 1 MATHEMATICS

6. Lesson 2.C Solving Quadratic Equations by Completing the Square MATHEMATICS

7. The product of a number and four less than the number is equal to 2. What is the number? MATHEMATICS

8. The number can be written as x ( x-4 ) = 2 Standard form x² - 4x -2 = 0 MATHEMATICS

9. The expression x² - 4x – 2 = 0 cannot be factored. MATHEMATICS

10. We can apply another method to solve the roots of the quadratic equation by Completing the Square . MATHEMATICS

11. The number can be written as x ( x-4 ) = 2 Standard form x² - 4x -2 = 0 MATHEMATICS

12. Using this method means transforming one side of the equation into a perfect square trinomial. MATHEMATICS

13. Example of perfect square trinomial 1. x ² + 4x + 4 factor (x + 2) (x + 2) or (x + 2)² 2. x² + 12x + 36 (x + 6) (x + 6) or ( x + 6 )² 3. x ² – 16x + 64 (x – 8) (x - 8) or (x – 8) ² It can form a square of binomial. MATHEMATICS

14. Steps in finding the roots of a quadratic equation by completing the square: 1.If the value of a is 1, proceed to step 2. Otherwise, divide both sides of the equation by the coefficient/value of a . MATHEMATICS

15. Find the roots of x ² - 4x – 2 = 0 by completing the square. MATHEMATICS

16. 2. Group all variable terms on the left side of the equation and the constant term is on the right side. x² - 4x = 2 MATHEMATICS

17. 3.Add the square of one-half of the coefficient of b ( 2nd term ) on both sides of the resulting equation. The left side of the equation becomes a perfect square trinomial. MATHEMATICS

18. x ² - 4x = 2 ½ (4) = 2 2²= 4 x ² - 4x + 4 = 2 + 4 x² - 4x + 4 = 6 MATHEMATICS

19. 4. Express the perfect square trinomial on the left side of the equation as a square of binomial. x² - 4x + 4 = 6 ( x - 2 )² = 6 MATHEMATICS

20. 5.Solve the resulting quadratic equation by extracting square root. ( x - 2 ) = 6 x - 2 = ± √6 MATHEMATICS

21. 6. Solve the resulting linear equations. + √6 - √6 x - 2 = √6 x - 2 =- √6 x = 2+ √6 x = 2- √6 MATHEMATICS

22. Example: 1. 2 x ² + 8x - 10 = 0 MATHEMATICS

23. Application: MATHEMATICS

24. Look for a partner and find the solution of each of the following quadratic equations by completing the the square. MATHEMATICS

25. a. x ² - 2x = 3 b. s² + 4s – 21 = 0 c. t² + 10t + 9 = 0 MATHEMATICS

26. Evaluation: MATHEMATICS

27. Group Activity: Write the indicated letter in the box that corresponds to the solutions of the quadratic equations by completing the square MATHEMATICS

28. MATHEMATICS “ IN TIME OF DIFFICULTIES, BE LIKE A _______ TREE.”

29. . MATHEMATICS