1. Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313 Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant to determine the number and type of roots of a quadratic equation.

2. Quadratic Formula The solutions of a quadratic equation of the form ax² + bx + c = 0, where a ≠ 0, are given by the following formula. To solve quadratic equations using the quadratic formula, the equation must be set equal to ZERO

3. Example 1: Solve by using the quadratic formula. 1. x² - 8x = 33

4. 2. x² - 34x + 289 = 0

5. 3. x² - 6x + 2 = 0

6. 4. x² + 13 = 6x

7. Discriminant: To find the number and types of roots of a quadratic equation use b² - 4ac b² - 4ac > 0; 2 real rational roots b² - 4ac is perfect square b² - 4ac > 0; 2 real irrational roots b² - 4ac is not a perfect square b² - 4ac = 0; 1 real rational root b² - 4ac < 0; 2 complex roots

8. Ex. 2: Describe the roots using the discriminant. 1. x² + 6x + 9 = 0 2. x ² + 3x + 5 = 0

9. 3. x² + 8x – 4 = 0 4. x² - 11x + 10 = 0