Ch-2 Lecture notes on Quadratic Functions.pptx

Quadratic Functions

1. Future Pure Mathematics Lecture 4 3 rd Batch PF101M

2. CHAPTER 2 THE QUADRATIC FUNCTION

3. Learning Objectives FACTORISE QUADRATIC EXPRESSIONS WHERE THE COEFFICIENT OF IS GREATER THAN 1 COMPLETE THE SQUARE AND USE THIS TO SOLVE QUADRATIC EQUATIONS SOLVE QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA  

4. Starter Activities Answers

5. Starter Activities Answers

6. Answers Starter Activities

7. Factorise Quadratic Expressions Where the Coefficient of is Greater than 1x   Example 1 Factorize Find two numbers : They must add together to make +5 and they must multiply together to give – 6 and  

8. Example 2 Factorize 4. Solution Find two numbers : They must add together to make -5 and they must multiply together to give – 24. 24 and  

9. Exercise 1 Exercise 1

10. Complete the Square and Use this to Solve Quadratic Equations The completing the square form Similarly, Completing the square:  

11. Complete the square for   Example 3 (b)  

12. Any quadratic equation can be solved by completing the square (a) he solutions of are either   Example 4 Complete the square to solve

13. (b) So the roots are (or)   Example 4

14. EXERCISE 2

15. SOLVE QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA The Quadratic formula Can be used to solve any quadratic equation of the form  

16. Use the quadratic formula to solve   Solution   Example 5

17. Exercise 3

18. Learning Objectives UNDERSTAND AND USE THE DISCRIMINANT TO IDENTIFY WHETHER THE ROOTS ARE ( i ) EQUAL AND REAL , (ii) UNEQUAL AND REAL OR (iii) NOT REAL UNDERSTAND THE ROOTS AND AND HOW TO USE THEM  

19. Use the Discriminant to Identify whether the Roots are (i) Equal and Real, (ii) Unequal and Real or (iii) Not Real The equation has two solutions and is called the discriminant .   Discriminant Roots of equation If real and unequal If real and equal If no real roots Discriminant Roots of equation real and unequal real and equal no real roots

20. What can you deduce from the value of the discriminants of these equations? Find the roots where possible. (a) 2 (b) 3 (c) 4 Solution 2 Therefore, there are no real roots . (b) Solution 3 Therefore, there are two unequal roots . So   Example 6

21. (c) Solution 4 Therefore, the roots are real and equal.  

22. The equation has two roots. What can you deduce about the value of the constant k?   Solution Since the equation has two roots   Example 7

23. Exercise 4

24. UNDERSTAND THE ROOTS AND AND HOW TO USE THEM   If and are the roots of the equation then you deduce that Comparing with For the equation The sum of roots, The product of the roots,  

25. The roots of the equation are and . Find an expression for and an expression for Hence find the repression for and an expression for Find a quadratic equation with roots and (a) Solution Therefore the sum of the roots And product of the roots   Example 8

26. (b) Substitute the values (c) Let the equation be So, the equation is Or    

27. The roots of the equation are and Without finding the value of and . (a) (b) (c)   Example 8 Solution If and are the roots of Then and If the roots are 3 then Sum of the roots Product of the roots Equation is        

28. (b) If the roots are Sum of the roots Product of the roots Equation is (c) If the roots are then Sum of roots Product of roots Therefore, equation is   and    

29. Exercise 5

30. Summary for Chapter 2

31. Exam Practice: Chapter 2