2. Deriving the Quadratic Formula Complete the square for the general case and solve for x : Continued….

3. Deriving the Quadratic Formula Continued….

4. Deriving the Quadratic Formula Voila! The Quadratic Formula

5. Using the Quadratic Formula The solution of the quadratic equation ax 2 + bx + c = 0 can be found by using the quadratic formula: These solutions are called the roots or zeroes of the equation!

6. Examples: 1.Solve 2x 2 – 5x + 2 = 0 2.Solve x 2 – 6x + 7 = 0 3.Solve x 2 – 5x + 7 = 0 4.Solve

7. SOLUTIONS 1. or

8. SOLUTIONS 2. or

9. SOLUTIONS 3. or

10. SOLUTIONS 4.

11. 5. A truck traveled from Calgary to Spokane (720 km). On the return trip, the average speed was increased by 10 km/h. If the total traveling time was 17 hours, what was the average speed from Calgary to Spokane? NOTE: TripDistanceSpeedTime Calgary to Spokane Spokane to Calgary TOTAL TIME 720 17 This column gives us our Quadratic Equation. Continued…

13. or This solution is inadmissible! The average speed from Calgary to Spokane was 80 km.hr.

14. HOMEWORK: Page 35 # 26 – 31 Page 57 # 59 & 60