1. 9.3 Solving Quadratic Equations by the Quadratic Formula

2. Solving Quadratic Equation by Completing the Square

3. Solving Quadratic Equation by Completing the Square

4. Your Turn This is (x + 2) 2. Form perfect trinomial squares by adding an appropriate term. x 2 + 4x x 2 – 6x x 2 – 5x This is (x – 3) 2.

5. Solve by Completing the Square

6. Example Solve by completing the square: 4x 2 –3 = –4x Solution: 4x 2 –3 = –4x 4x 2 + 4x – 3 = 0

7. Example – Solution We then use completing the square to solve the equation. cont’d or

8. Quadratic Formula

9. Derivation of the Quadratic Formula

10. Derivation of the Quadratic Formula

11. Derivation of the Quadratic Formula

12. Derivation of the Quadratic Formula

13. Example

14. Your Turn

15. Determine if a quadratic equation has real- number solutions

16. A TV screen is 46-inch wide. The 46-inch screen is measured along the diagonal. The screen is rectangular in shape and is 17 inches wider than is is high. Find the dimensions of a screen. Solution: 1.Let h = height Then, w = h + 17 2.Equation: h 2 + (h + 17) 2 = 46 2 Application