1 / 6

Revision - Quadratic Equations

Revision - Quadratic Equations. Solving Quadratic equations by the Quadratic Formula. By I Porter. For any quadratic equation ax 2 + bx + c = 0, where a ≠ 0,. Quadratic formula, a ≠0. Introduction.

carla-reed
Download Presentation

Revision - Quadratic Equations

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. Revision - Quadratic Equations Solving Quadratic equations by the Quadratic Formula. By I Porter

  2. For any quadratic equation ax2 + bx + c = 0, where a ≠ 0, Quadratic formula, a ≠0. Introduction The complete the square method of solving quadratic equations can be used to derive a formula to solve any quadratic equation. Proof: (not required for examination) For any quadratic equation ax2 + bx + c = 0, where a ≠ 0 Factorise LHS Rearrange RHS Divide throughout by ‘a’ Rearrange Take √ of both sides. If the term to complete the square LHS. Rearrange, x = ..

  3. For ax2 + bx + c = 0, then Example 1: Use the quadratic formula to solve. Always test on one you can factorise! x2 + 6x + 8 = 0 Write-out the substitution into formula a = +1, b = +6, c = +8 Evaluate as an exact value! Note: b2 - 4ac ≥ 0 for ax2 + bx + c = 0 to have solutions. This is called the discriminant.

  4. For ax2 + bx + c = 0, then Example 2: Use the quadratic formula to solve. 3x2 - 6x + 2 = 0 Write-out the substitution into formula a = +3, b = -6, c = +2 Evaluate as an exact value! Reduce all surds. Note: b2 - 4ac ≥ 0 for ax2 + bx + c = 0 to have solutions. This is called the discriminant.

  5. Evaluate as an exact value! For ax2 + bx + c = 0, then Quadratic Equation. Write-out the substitution into formula Correct to 2 decimal places. a = +1, b = -1, c = -1 Example 3: Use the quadratic formula to solve. Rearrange. You may have to give your answer correct a set number of decimal places or significant figures using your calculator to give an approximation.

  6. e) Exercise: Find exact solution to the following. a) x2 + 8x - 9 = 0 b) 2x2 - 6x - 5 = 0 c) 5x2 - x - 2 = 0 d) 4x2 - x - 1 = 5x + 4

More Related