2. Thought for the day The early bird gets the worm, but the second mouse gets the cheese.

5.  The ROOTS (or solutions) of a polynomial are its x- intercepts  Recall: The x- intercepts occur where y = 0 ROOTS

6.  Example: Find the roots:  Solution: Factoring:  The roots are:

7.  But what about NASTY trinomials that don’t factor?  After centuries of work, mathematicians realized that as long as you know the coefficients, you can find the roots of the quadratic. Even if it doesn’t factor!!!!  This is done using the Quadratic Formula

8. “x equals negative b plus or minus the square root of b squared minus four a-c all over two a!!!” http://www.youtube.com/watch?v=79F2QxpjBz0 http://www.youtube.com/watch?v=BfN0n0woey4&feature=related http://www.youtube.com/wa tch?v=pBKgCx_Q0hY&feat ure=related

9. Example 1 Use the quadratic formula to solve the equation : x 2 + 5x + 6= 0 Solution: x 2 + 5x + 6= 0 a = 1 b = 5 c = 6 x = - 2 or x = - 3 These are the roots of the equation.

10. x 2 + 5x + 6 = 0 x = - 2 or x = - 3

11. 

16. SUMMARY OF SOLVING QUADRATIC EQUATIONS

18. Discriminant: How many Solutions Are There?

20. Solutions of a Quadratic Equation

23. Let where a ≠ 0. ▫ If, then the quadratic equation has 2 distinct real solutions ▫ If, then the equation has 1 real solution, a double root ▫ If, then the equation has 0 real solutions

24. EXAMPLES: Find the discriminant for each equation. Then determine the number of real solutions for each equation by using the discriminant.