2-Solving-Quadruijyyyyyyyyyyatic-Equations.pptx

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1. SOLVING QUADRATIC EQUATIONS Extracting Square Roots Factoring Completing the Square Quadratic Formula DOMINIC DALTON L. CALING Mathematics | Grade 9

2. Any value that satisfies an equation is called a solution . The set of solution that satisfy an equation is called solution set . The solution is also called root . In solving quadratic equations, it means finding its solution(s) or root(s) that will satisfy the given equation.

3. Solving Quadratic E q uation by Extracting the S q uare Roots

4. LET’S PRACTICE  

5. SQUARE ROOT PROPERTY For any real number n If , then or and .  

6. Reminder: Before using the square root property, make sure that the equation is in the form .  

7. Steps in Solving Quadratic Equation by Extracting the Square Root Write the equation in the form . Use the square root property. Solve for x .  

8. EXAMPLE 1:  

9. EXAMPLE 2 :  

10. EXAMPLE 3:  

11. EXAMPLE 4 :  

12. EXAMPLE 5:  

13. EXAMPLE 6 :  

14. Solving Quadratic E q uation by Factoring

15. Steps in Solving Quadratic E q uation by Factoring Write the quadratic equation in standard form. Find the factors of the quadratic expression. Apply the Zero Product Property . Solve each resulting equation. Check the values of the variable obtained by substituting each in the original equation.

16. Zero Product Property The product AB = 0, if and only if A = 0 or B = 0.

17. EXAMPLE 1:  

18. EXAMPLE 2 :  

19. EXAMPLE 3:  

20. EXAMPLE 4 :  

21. EXAMPLE 5 :  

22. Solving Quadratic Equation by Completing the Square

23. Steps in Solving Quadratic E q uation by Completing the S q uare If the value of a = 1, proceed to step 2. Otherwise, divide both sides of the equation by a . Group all the terms containing a variable on one side of the equation and the constant term on the other side. That is Complete the square of the resulting binomial by adding the square of the half of b on both sides of the equation.  

24. Rewrite the perfect square trinomial as the square of binomial. Use extracting square the square root to solve for x .   Steps in Solving Quadratic E q uation by Completing the S q uare

25. EXAMPLE 1:                                  

26. EXAMPLE 2 :                                  

27. EXAMPLE 3:  

28. Solving Quadratic E q uation by the Quadratic Formula

29. QUADRATIC FORMULA 𝒙 = −𝒃 ± 𝒃 𝟐 − 𝟒𝒂𝒄 𝟐𝒂

30. EXAMPLE 1:                          

31. EXAMPLE 2 :                             STANDARD FORM