M1L1 Illustrations of Quadratic Equations.pptx

This is a presentation of the lesson on Illustrations of Quadratic Equations for quarter I of Mathematics Grade 9 level. In this lesson, the students will be able to differentiate quadratic equations and linear equations, change the quadratic equation in its standard form, and identify the values of a, b, and c. The students will also be able to apply the concept of quadratic equations in real-life situations.

1. Lesson 1: Illustrations of Quadratic Equations Quadratic Equations /mylynddetorres/

2. Activity 1: Do You Remember These Products? Find each indicated product then answer the questions that follow.           How would you describe the products obtained? Are the products polynomials? If YES, what common characteristics do these polynomials have?

3. / mylynddetorres / What are the different landforms in Asia? Compare kapatagan and bulubundukin in terms of its look. Which do you think represents a linear equation? Let’s Start!

4.                       / mylynddetorres / Identify the equations as to linear or not linear. Group them with the two of the landforms in Asia, kapatagan and bulubundukin . Write the linear equations in column KAPATAGAN and not linear in column BULUBUNDUKIN . Activity 2: Another Kind of Equation!  

5.                       / mylynddetorres / LINEAR EQUATIONS Activity 2: Another Kind of Equation!   NOT LINEAR EQUATIONS

6. / mylynddetorres / 1. Which of the given equations is linear? 3. Which of the given equations is not linear? Why? How are these equations different from those which are linear? What common characteristics do these equations have? Activity 2: Another Kind of Equation! 2. How do you describe linear equations?

7. Quadratic Equation A mathematical sentence of degree 2 that can be written in the following standard form constant term / mylynddetorres / ax 2 +bx+c=0 a≠0 quadratic term linear term a b c real numbers

8. Example 1: Write the quadratic equations in standard form and give the values of a, b, and c. /mylynddetorres/ 2x 2 +5x-3=0 b = 5 c = -3 a = 2

9. Example 2: Write the quadratic equations in standard form and give the values of a, b, and c. /mylynddetorres/ 3x(x-2)=0 b = -6 c = 0 a = 3 3x 2 – 6x=0

10. Example 3: Write the quadratic equations in standard form and give the values of a, b, and c. /mylynddetorres/ (2x+5)(x-1) = -6 b = 3 c = 1 a = 2 2x 2 -2x+5x-5 +6 =-6 +6 2x 2 +3x+1=0

11. Example 4: Write the quadratic equations in standard form and give the values of a, b, and c. /mylynddetorres/ x 2 +5=0 b = 0 c = 5 a = 1

12. Example 5: Write the quadratic equations in standard form and give the values of a, b, and c. /mylynddetorres/ -2x 2 +7=0 b = 0 c = 7 a = -2

13. Example 6: Write the quadratic equations in standard form and give the values of a, b, and c. /mylynddetorres/ -9=16x 2 b = 0 c = 9 a = 16 16x 2 +9=0 16x 2 +9 =-9 +9

14. Group Activity: Am I Quadratic or Not /mylynddetorres/           Identify which of the following equations are quadratic and which are not. If the equation is quadratic, write in standard form and give the values of a, b, and c.

15. /mylynddetorres/ Not Quadratic   Group Activity: Am I Quadratic or Not Identify which of the following equations are quadratic and which are not. If the equation is quadratic, write in standard form and give the values of a, b, and c.

16. /mylynddetorres/ Not Quadratic   Group Activity: Am I Quadratic or Not Identify which of the following equations are quadratic and which are not. If the equation is quadratic, write in standard form and give the values of a, b, and c.

17. /mylynddetorres/ Quadratic       Group Activity: Am I Quadratic or Not Identify which of the following equations are quadratic and which are not. If the equation is quadratic, write in standard form and give the values of a, b, and c.

18. /mylynddetorres/ Quadratic       Group Activity: Am I Quadratic or Not Identify which of the following equations are quadratic and which are not. If the equation is quadratic, write in standard form and give the values of a, b, and c.

19. /mylynddetorres/ Quadratic       Group Activity: Am I Quadratic or Not Identify which of the following equations are quadratic and which are not. If the equation is quadratic, write in standard form and give the values of a, b, and c.

20. APPLICATION : Does It Illustrate Me /mylynddetorres/ 1. The length of a swimming pool is 8 m longer than its width and the area is 105 m 2 . 2. Edna paid at least Php1,200 for a pair of pants and a blouse. The cost of the pair of pants is Php600 more than the cost of the blouse. 3. A garden 7 m by 12 m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92 m 2 . Tell whether each of the following situations illustrates quadratic equations or not. Justify your answer by representing each situation by a mathematical sentence.

21. /mylynddetorres/ 1. The length of a swimming pool is 8 m longer than its width and the area is 105 m 2 .   Quadratic   APPLICATION : Does It Illustrate Me Tell whether each of the following situations illustrates quadratic equations or not. Justify your answer by representing each situation by a mathematical sentence.

22. /mylynddetorres/ 2. Edna paid at least Php1, 200 for a pair of pants and a blouse. The cost of the pair of pants is Php600 more than the cost of the blouse.     Not Quadratic APPLICATION : Does It Illustrate Me Tell whether each of the following situations illustrates quadratic equations or not. Justify your answer by representing each situation by a mathematical sentence.

23. /mylynddetorres/ 3. A garden 7 m by 12 m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92 m 2 .     Quadratic APPLICATION : Does It Illustrate Me Tell whether each of the following situations illustrates quadratic equations or not. Justify your answer by representing each situation by a mathematical sentence.

24. GENERALIZATION: /mylynddetorres/ Fill in the blanks. A quadratic equation in one variable is a mathematical sentence of degree __________ that can be written in the following standard form. __________ where a, b, and c are real numbers and a ≠ 0    

25. GENERALIZATION: /mylynddetorres/ Fill in the blanks. 2. In the equation ax 2 + bx + c = 0, ax 2 is the __________ term, bx is the __________ term, and c is the __________ term.      

26. EVALUATION /mylynddetorres/ Answer the questions correctly. 1. TRUE or FALSE: is a quadratic equation.   2. TRUE or FALSE: In the quadratic term is 3x.   3. In the quadratic equation , the constant term is _____.   4. Write the quadratic equation in its standard form.   5. Find the value of b in the quadratic equation .  

27. ASSIGNMENT /mylynddetorres/ Answer additional exercises by joining in a Wordwall quiz/game using the link below. https://wordwall.net/play/34945/865/326 (Take a screenshot on the part where score and name are visible and send it to the class’s FB Messenger group). Note: You can also watch the video lesson for this topic before answering the activities. The video link will be posted by the teacher in the FB private group of grade 9 students. https://www.youtube.com/watch?v=lOvVNvGcnJU https://www.youtube.com/watch?v=w5e9XiyyZrA

28. Thank you for listening! /mylynddetorres/ by: MYLYN D. DE TORRES Mathematics 9 Teacher