1. Lesson 9.8

2. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2

3. California Standards 19.0 Students know the quadratic formula and are familiar with its proof by completing the square. 20.0 Students use the quadratic formula to find the roots of a second- degree polynomial and to solve quadratic equations.

5. In the previous lesson, you completed the square to solve quadratic equations. If you complete the square of ax 2 + bx + c = 0, you can derive the Quadratic Formula.

6. 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 :

7. 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.

8. Example 2 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.

9. 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.

10. Because the Quadratic Formula contains a square root, the solutions may be irrational. You can give the exact solution by leaving the square root in your answer, or you can approximate the solutions.

11. 1. Solve x 2 + x = 12 by using the Quadratic Formula. 2. Solve –3x 2 + 5x = 1 by using the Quadratic Formula. 3. Solve 8x 2 – 13x – 6 = 0. Use at least 2 different methods. Lesson Quiz 3, –4 = 0.23, ≈ 1.43