1. SWBAT… use the Quadratic Formula to solve quadratic equations Tues, 2/14 Happy Valentine’s Day! Agenda 1. WU (10 min) 2. Quadratic Formula (25 min) 3. Exit slip (10 min) Warm-Up: Find the solutions: 1. 8x 2 + 2x – 3 = 0 2. 2x 2 – 6x + 3 = 0 HW#8: Solving Quadratic Equations by Graphing: Baseball Path

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 the equation 8x 2 + 2x – 3= 0 Solution: 8x 2 + 2x – 3 = 0 a = 8 b = 2 c = -3 x = ½ or x = -¾ These are the roots of the equation.

6. Use the Quadratic Formula to find the exact solutions of the equations 2x 2 – 6x + 3 = 0 a = 2 b = -6 c = 3 Example 2 These are the roots of the equation.

7. Example 4 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 Example 5 These are the roots of the equation.

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 5: Correct Solution These are the roots of the equation.

10. This will be collected – complete on a sheet of paper: 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 These are the roots of the equation. 2.) Use factoring to solve x 2 + 5x + 6 = 0