Lesson 1 and 2 solving QE by factoring and extracting the roots Math 9.pptx

factoring

1. QUADRATIC EQUATION

2. REVIEW Tell me about their previous knowledge about equation and their Properties

3. Equation An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

4. Quadratic Equation in One Variable A second-degree equation in one variable an equation that can be expressed in the form Where a, b, and c are real numbers, and a≠0. This form of the Quadratic Equation is said to be in Standard Form  

5. Two classifications of quadratic equations in two variables according to the value of b in the standard form. If b≠0, the equation is complete quadratic equation . Example: If b=0, the equation is a pure or incomplete quadratic equation For Instance:  

6. Activity 1 Transform each equation in standard form. Then, identify the values of a, b, and c.  

7. Activity 2: Solve each equation.  

8. Solving Equations by Extracting Square Roots Note that the incomplete quadratic equation can be written as by applying Addition Property of Equality. By substitution, two values of x satisfy this equation. This are 2 and-2. To check, if and x=2, then  

9. Solving Equations by Extracting Square Roots Note that the incomplete quadratic equation can be written as by applying Addition Property of Equality. By substitution, two values of x satisfy this equation. This are 2 and-2. To check, if and x=2, then Note that √4=2 or √4=-2.      

10. Square Root Property  

11. Example 1: Solve the equation     Check: If x=5, If x=-5 Therefore, the solution are 5 and-5  

12. Solving Quadratic Equations by Factoring The test for factorability of a trinomial of the form states that the discriminant is perfect square, For instance, the trinomial where a=1,b=-8 and c=12, is factorable since is perfect square,  

13. Solving Quadratic Equations by Factoring In fact , However, the trinomial where a=2,b=-13 and c=12 is not factorable since,  

14. Square Root Property The product  

15. Activity 1: Solve the equation          

16. Activity 1: Solve the equation   If   If      

17. Example 2 Solve the equation      

18. Solve the following quadratic equations by factoring.   Give the roots of the equation.  

19. Solve the following quadratic equations by factoring.   Give the roots of the equation.  

20. Thank you for Listening