solving quadratic equation by completing the square.pptx

mathematics 9

1. Solving Quadratic Equations by Completing the Square

2. Objectives Express square of trinomials as a square of binomials; and Solve quadratic equations by completing the square

3. Activity: Express each of the following perfect square trinomials as a square of binomial. 1. x 2 + 4x + 4 2. t 2 + 12t + 36 3. s 2 + 10s + 25 4. x 2 - 16x + 64 5. h 2 -14x + 49 6.  

4. QuQ Question How do you describe a perfect square trinomial?

5. QuQ Question How did you express each perfect square trinomials as the square of a binomial?

6. Activity: Make it perfect!!! 1. x 2 + 2x + ____ 2. t 2 + 20t +_____ 3. r 2 + 24r + ___ 4. x 2 - 16x + ___ 6. ___   Determine a number that must be added to make each of the following a perfect square trinomial. 5. ___  

7. QuQ Another method of solving quadratic equations is by completing the square . This method involves transforming the quadratic equation ax 2 + bx + c = 0 into the form (x-h) 2 = k , where k 0.  

8. QuQ To solve the quadratic equation ax 2 + bx + c = 0 by completing the square, the following steps can be followed: 1. Divide both sides of the equation by a then simplify. 2. Write the equation such that the terms with variables are on the left sides of the equation and the constant term is on the right side.

9. QuQ 3. Add the square of one-half of the coefficient of x on both sides of the resulting equation. The left side of the equation becomes a perfect square trinomial. 4. Express the perfect square trinomial on the left side of the equation as a square of a binomial. 5. Solve the resulting quadratic equation by extracting the square root.

10. QuQ 6. Solve the resulting linear equations. 7. Check the solutions obtained against the original equation.

11. QuQ Example 1: Solve the quadratic equation 2x 2 + 8x – 10 = 0 by completing the square.

12. QuQ Step 1. Divide both sides of the equation by a then simplify. 2x 2 + 8x – 10 = 0 =   x 2 + 4x – 5 = 0

13. QuQ Step 2 x 2 + 4x – 5 = 0 x 2 + 4x = 5

14. QuQ Step 3 x 2 + 4x = 5     4 x 2 + 4x + 4 = 5 + 4 x 2 + 4x + 4 = 9

15. QuQ Step 4 x 2 + 4x + 4 = 9 ( x + 2) 2 = 9

16. QuQ Step 5 ( x + 2) 2 = 9       x + 2 =  

17. QuQ Step 6 x + 2 =   x + 2 = +3 x = +3 - 2 x = 1 x + 2 = -3 x = -3 - 2 x = -5

18. QuQ Example 1: Solve the quadratic equation 4x 2 - 32x +28 = 0 by completing the square.

19. QuQ Example 1: Solve the quadratic equation x 2 - 2x = 3 by completing the square.

20. QuQ Quiz: Find the solutions of each of the following quadratic equations by completing the square. 1. s 2 +4s - 21 = 0 2. x 2 +10x +9 = 0 3. x 2 +14x = 32