Nature of Roots of the Quadratic EquationCO1-2024-2025.pptx

Nature of Roots of the Quadratic Equation

1. Welcome to OUR math class ! Ma’am Jen

2. Prayer Greetings Checking of Attendance Classroom Management Respect Others Treat classmates and teachers with kindness and consideration. Listen when someone else is speaking, and avoid interrupting. Be Prepared Bring all necessary materials to class, such as paper, ballpen, notebooks, and any completed homework. Follow Directions Pay attention to instructions from the teacher and follow them carefully Raise Your Hand If you have a question or wish to contribute to the discussion, raise your hand and wait to be called on. Stay on Task Focus on the assignment or activity at hand and avoid distractions such as using your phone or talking off-topic. Review of the Past Lesson

3. Review of the past lesson 1. Rational numbers are numbers that can be written in the form p/q where q is not equal to zero. 1 Yes – NO – Stand Up Game A ctivity

4. 1 Yes – NO – Stand Up Game Review of the past lesson 2. The decimal number 0.98765498653921… is an example of rational number. A ctivity

5. 1 Yes – NO – Stand Up Game Review of the past lesson 3. Terminating and Non-terminating but repeating are words that best describe rational numbers. A ctivity

6. AWARENESS: Direction: Given the situations below, identify if the statement is REAL or Not REAL. If the situation is REAL say “YES”, if the situation is Not REAL say “NO”. 2 Real or Not Real A ctivity 1. The LGBT community is given the same rights with men and women of today’s generation.

7. SPIN

8. AWARENESS: Direction: Given the situations below, identify if the statement is REAL or Not REAL. If the situation is REAL say “YES”, if the situation is Not REAL say “NO”. 2 Real or Not Real A ctivity 1. The LGBT community is given the same rights with men and women of today’s generation.

9. AWARENESS: 2 Real or Not Real A ctivity 2. Same sex marriage is allowed in the Philippines .

10. SPIN

11. AWARENESS: 2 Real or Not Real A ctivity 2. Same sex marriage is allowed in the Philippines .

12. AWARENESS: 2 Real or Not Real A ctivity 3. LGBT community has the privilege to live free from violence and discrimination. .

13. SPIN

14. AWARENESS: 2 Real or Not Real A ctivity 3. LGBT community has the privilege to live free from violence and discrimination. .

15. AWARENESS: 2 Real or Not Real A ctivity 4. Gays and Lesbians are not allowed to enroll in any educational or training institution .

16. SPIN

17. AWARENESS: 2 Real or Not Real A ctivity 4. Gays and Lesbians are not allowed to enroll in any educational or training institution .

18. AWARENESS: 2 Real or Not Real A ctivity 5. Discrimination and bullying of gay and transgender people remain a threat to LGBT freedom and welfare.

19. SPIN

20. AWARENESS: 2 Real or Not Real A ctivity 5. Discrimination and bullying of gay and transgender people remain a threat to LGBT freedom and welfare.

21. ARE YOU NOW READY?

22. THE NATURE OF ROOTS Of a QUADRATIC EQUATION

23. . B1. ACTIVITY: 3 A ctivity Unveiling the Nature of Quadratic Roots (Group Activity) Instruction: Complete the table below by solving b 2 – 4ac. Group Quadratic Equation Values of a, b, and c Substitute b 2 -4ac Answer Group I x 2 + 2x + 3 = 0 a= b= c=     Group II x 2 – 2x – 2 = 0 a= b= c=     Group III x 2 + 5x + 4 = 0 a= b= c=     Group IV x 2 + 4x + 4 = 0 a= b= c=    

24. Let’s check your work!

25. . B1. ACTIVITY: 3 A ctivity Let’s Solve Instruction: Complete the table below by solving b 2 – 4ac. Group Quadratic Equation Values of a, b, and c Substitute b 2 -4ac Answer Group I x 2 + 2x + 3 = 0 a=1 b=2 c=3  2 2 - 4(1)(3) 4-12  -8 Group II x 2 – 2x – 2 = 0 a=1 b=-2 c=-2 (-2) 2  -4(1)(-2) 4-(-8) 12  Group III x 2 + 5x + 4 = 0 a=1 b=5 c=4 5 2 -4(1)(4)  25-16 9  Group IV x 2 + 4x + 4 = 0 a=1 b=4 c=4   4 2 -4(1)(4) 16-16 0 

26. . B1. ACTIVITY: 4 A ctivity Let’s Solve (Group Activity Instruction: Solve for the roots of the quadratic equation u sing the sa me equation assigned to each group . x 2 + 2x + 3 = 0 x 2 + 4x + 4 = 0 x 2 + 5x + 4 = 0 x 2 – 2x – 2 = 0 GROUP 1 GROUP 4 GROUP 3 GROUP 2

27. DISCUSSION The value of the expression b 2 - 4ac is called the discriminant of the quadratic equation, denoted by D = b 2 – 4ac. This value can be used to describe the nature of the roots of a quadratic equation. It can be zero, positive perfect square, positive but not a perfect square, or negative. • If D = 0 , the roots are real and are equal • If D > 0 and a perfect square , the roots are rational but are not equal • If D > 0 and not a perfect square , the roots are irrational and are not equal • If D < 0 , the equation has no real roots.  

28. B3. analysis How did you get your answer/s? 2. How would you describe the roots of a quadratic equation when b 2 – 4ac is zero? Perfect square? Not a perfect square? Negative? 3. Which of the quadratic equation has roots that are not equal? Equal? Rational numbers? Irrational numbers? 4. Is there a need to solve for b 2 – 4ac? Why?

29. ION B4. aBSTRACTION How can we describe the nature of the roots of a quadratic equation? What are the steps? How can you describe the roots of a quadratic equation if the discriminant is equal to 0? Less than 0? Greater than 0 and a perfect square? Greater than 0 and not a perfect square? Why is it important to know and understand the nature of roots of the quadratic equation? What are some real-life scenarios where nature of roots can be applied?

30. . B5. APPLICATION 5 A ctivity Real-Life Application Directions: Given the situation below, answer the question using the guide questions.   Situation: Marcus kicks a football in order to score a field goal. The height of the ball is given by the equation y = - x 2 + x, where y is the height of the goalpost. If the goalpost is 10 feet high, can Marcus kick the ball high enough to go ever the goalpost?   Guide Questions: 1. What will be the resulting equation in standard form? Hint: replace y by 10 (the height of the goalpost)   2. What is the value of the discriminant? Hint: use the equation in standard form in no.1   3. Would it be possible for Marcus to kick the ball high enough to go over the goalpost? Hint: if the discriminant is positive – it is possible If the discriminant is negative – it is not possible

31. ASSESSMENT: Direction: Describe the nature of the roots of the following quadratic equations using the discriminant. A. real and are equal B. rational but are not equal C. irrational and are not equal D. no real roots.  

32. ASSIGNMENT: Reinforcement Activity With the same group used in the previous activity, describe the nature of roots using the value of the discriminant through: Yell(musical)-Group 1, Reporting (talk show)-Group 2, Group discussion (classroom setting)-Group 3, Oral reading- Group 4.

33. THANK YOU!