2. First, set y = 0 Continued…. Divide Both sides by “a”.

3. Now Complete the Square: Isolate the Perfect Square

4. Factor the Perfect Square Move the extra terms to the other side.

5. Find a Common Denominator And Simplify.

6. Take the Square Root of Both Sides. Make sure both signs are included!

7. This gives the following result. Subtract the constant from both sides

8. Simplify Such is the Quadratic Formula!

9. 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!

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

11. SOLUTIONS 1. or

12. SOLUTIONS 2. or

13. SOLUTIONS 3. or

14. SOLUTIONS 4.

15. 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…

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

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