1 / 94

6.5 – Solving Equations with Quadratic Techniques

6.5 – Solving Equations with Quadratic Techniques. Quadratic equations are in the form: a x 2 + b x + c ,. Quadratic equations are in the form: a x 2 + b x + c , where a, b, & c are integers. Quadratic equations are in the form: a x 2 + b x + c , where a, b, & c are integers exs. .

cassandra-lott
Télécharger la présentation

6.5 – Solving Equations with Quadratic Techniques

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. 6.5 – Solving Equations with Quadratic Techniques

  2. Quadratic equations are in the form: ax2 + bx + c,

  3. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers

  4. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs.

  5. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2

  6. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2 • 2x2 – 18x + 13

  7. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2 • 2x2 – 18x + 13 • x2 – 9

  8. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2 • 2x2 – 18x + 13 • x2 – 9 x2+ 0x – 9

  9. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2 • 2x2 – 18x + 13 • x2 – 9 x2+ 0x – 9 • 2x2 + 8x

  10. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2 • 2x2 – 18x + 13 • x2 – 9 x2+ 0x – 9 • 2x2 + 8x 2x2 + 8x+ 0

  11. Quadratic equations are in the form: ax2 + bx + c, where a, b, & c are integers exs. • x2 + 5x + 2 • 2x2 – 18x + 13 • x2 – 9 x2+ 0x – 9 • 2x2 + 8x 2x2 + 8x+ 0 NOTE: Must have the “x2” term to be a quadratic!

  12. Ex. 1 Write each expression in quadratic form, if possible.

  13. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36

  14. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2

  15. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2)

  16. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36

  17. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36

  18. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625

  19. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2

  20. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2 – 625

  21. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2 – 625 c. x½– 9x¼ + 16

  22. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2 – 625 c. x½– 9x¼ + 16 (x¼)2

  23. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2 – 625 c. x½– 9x¼ + 16 (x¼)2– 9(x¼)

  24. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2 – 625 c. x½– 9x¼ + 16 (x¼)2– 9(x¼) + 16

  25. Ex. 1 Write each expression in quadratic form, if possible. a. x4 + 13x2 + 36 (x2)2 + 13(x2) + 36 b. 16x6 – 625 (4x3)2 – 625 c. x½– 9x¼ + 16 (x¼)2– 9(x¼) + 16

  26. Ex. 2 Solve each equation. a. x4 = 16

  27. Ex. 2 Solve each equation. a. x4 = 16 -16 -16

  28. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0

  29. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0

  30. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0

  31. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0

  32. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 )(x2 ) = 0

  33. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0

  34. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0

  35. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0

  36. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0

  37. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 (x )(x ) = 0

  38. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0

  39. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0

  40. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2

  41. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

  42. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

  43. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

  44. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 ORx2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

  45. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 ORx2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 x = 2 OR x = -2

  46. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 ORx2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 √x2 = √-4 x = 2 OR x = -2

  47. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 ORx2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 √x2 = √-4 x = 2 OR x = -2 OR x = ±2i

  48. Ex. 2 Solve each equation. a. x4 = 16 -16 -16 x4 – 16 = 0 (x2)2 – 16 = 0 ( )( ) = 0 (x2 – 4)(x2 + 4) = 0 x2 – 4 = 0 ORx2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 ORx2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x2 = -4 +2 +2 -2 -2 √x2 = √-4 x = 2 OR x = -2 OR x = ±2i

  49. b. x4 + 11x2 + 18 = 0

  50. b. x4 + 11x2 + 18 = 0

More Related