1. Using the factoring method, what are the solutions of y = x 2 + 5x + 6

2. The Quadratic Formula YOU MUST MEMORIZE THIS FORMULA!!!

4. What Does The Formula Do? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise. The formula states that for a quadratic equation of the form : ax 2 + bx + c = 0 The roots of the quadratic equation are given by :

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

6. Example 2 Use the quadratic formula to solve: 8x 2 + 2x – 3 = 0 Solution: 8x 2 + 2x – 3 = 0 a = 8 b = 2 c = -3 x = ½ or x = -¾

7. Example 3 Use the quadratic formula to solve the equation 8x 2 – 22x + 15 = 0 Solution: 8x 2 – 22x + 15 = 0 a = 8 b = -22 c = 15 x = 3/2 or x = 5/4 These are the roots of the equation.

8. a = -2 b = 5 c = 3 x = ½ or x = -3/4 What is wrong with this student’s work? What are the correct solutions? Use the quadratic formula to solve the equation -2x 2 + 5x + 3= 0

9. a = -2 b = 5 c = 3 x = -2/4 = -1/2 or x = 3 Use the quadratic formula to solve the equation -2x 2 + 5x + 3= 0 Example 4

10. The Discriminant In the Quadratic Formula, the expression under the radical sign, b 2 – 4ac is called the discriminant. The discriminat can be used to determine the number of real solutions of a quadratic equation.

11. Key Concept: Using the Discriminant Equation Example Discriminant Graph of Related Function Number of Real Solutions

12. Key Concept: Using the Discriminant Equation Example x 2 + 2x + 5 = 0x 2 + 10x + 25 = 02x 2 – 7x + 2 = 0 Discriminant Graph of Related Function Number of Real Solutions

13. Key Concept: Using the Discriminant Equation Example x 2 + 2x + 5 = 0x 2 + 10x + 25 = 02x 2 – 7x + 2 = 0 DiscriminantNegativeZeroPositive Graph of Related Function Number of Real Solutions

14. Key Concept: Using the Discriminant Equation Example x 2 + 2x + 5 = 0x 2 + 10x + 25 = 02x 2 – 7x + 2 = 0 DiscriminantNegativeZeroPositive Graph of Related Function 0 x-intercepts1 x-intercepts2 x-intercepts Number of Real Solutions

15. Key Concept: Using the Discriminant Equation Example x 2 + 2x + 5 = 0x 2 + 10x + 25 = 02x 2 – 7x + 2 = 0 DiscriminantNegativeZeroPositive Graph of Related Function 0 x-intercepts1 x-intercepts2 x-intercepts Number of Real Solutions 012