1 / 11

The Quadratic Formula.

The Quadratic Formula. Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. . 1. x 2. 4. 2. xyz. 6 . 3. x 2 – yz. 4. y – xz. 7. 1 . 6. z 2 – xy. 5. – x. 7 . 2. California Standards.

elewa
Download Presentation

The Quadratic Formula.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Quadratic Formula. Lesson 9.8

  2. Warm Up Evaluate for x = –2, y = 3, and z = –1. 1. x2 4 2. xyz 6 3. x2 – yz 4. y – xz 7 1 6. z2 – xy 5. –x 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.

  4. In the previous lesson, you completed the square to solve quadratic equations. If you complete the square of ax2 + bx + c = 0, you can derive the Quadratic Formula.

  5. 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 : ax2 + bx + c = 0 The roots of the quadratic equation are given by :

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Lesson Quiz 1. Solve x2 + x = 12 by using the Quadratic Formula. 2. Solve –3x2 + 5x = 1 by using the Quadratic Formula. 3.Solve 8x2 – 13x – 6 = 0. Use at least 2 different methods. 3, –4 = 0.23, ≈ 1.43

More Related