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# Solving quadratic equations part 1

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• ### Solving quadratic equations part 1

1. 1. Solving Quadratic Equations PART 1
2. 2. Why do we need to solve Quadratic Equations?• View this Discovery Education video to see a use for Quadratic Equations AND why math is cool!
3. 3. Why do we need to solve Quadratic Equations?• View this Discovery Education video to see a use for Quadratic Equations AND why math is cool!• Now, wasn’t that cool? I bet you never look at a pumpkin the same way again!
4. 4. Why do we need to solve Quadratic Equations?• View this Discovery Education video to see a use for Quadratic Equations AND why math is cool!• Now, wasn’t that cool? I bet you never look at a pumpkin the same way again!• Let’s look at solving Quadratic Equations a little closer.
5. 5. What is a Quadratic Equation?• View this Cool Math lesson introducing Quadratic Equations.• There are 2 pages of notes.• Complete the Try It problems in your notebook and check your answers on the next slide.
6. 6. Page 2 - Try It 2 −3x − x − 5 = 0
7. 7. Page 2 - Try It 2• Find a, b, and c. −3x − x − 5 = 0
8. 8. Page 2 - Try It 2• Find a, b, and c. −3x − x − 5 = 0 a. -3 b. -1 c. -5
9. 9. Page 2 - Try It 2• Find a, b, and c. −3x − x − 5 = 0 a. -3 b. -1 c. -5 2• Find a, b, and c. x −6=0
10. 10. Page 2 - Try It 2• Find a, b, and c. −3x − x − 5 = 0 a. -3 b. -1 c. -5 2• Find a, b, and c. x −6=0 a. 1 b. 0 (The x term is missing so b is 0.) c. -6
11. 11. Solving Quadratic Equations by Factoring• View this Cool Math website to learn about solving Quadratic Equations.• There are 9 pages to view.• Complete the Try It problems in your notebook and check your answers on the next slides.
12. 12. Page 4 - Try It• Solve. 2 x + 8x + 12 = 0
13. 13. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial.
14. 14. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0
15. 15. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factorsand set equal to 0.
16. 16. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factorsand set equal to 0. x+6=0 or x+2=0
17. 17. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factorsand set equal to 0. x+6=0 or x+2=0 Solve each equation.
18. 18. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factorsand set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation.
19. 19. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factorsand set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation. x = −6 or x = −2
20. 20. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factorsand set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation. x = −6 or x = −2 Answer: {−6, −2}
21. 21. Page 5 - Try It & Your Turn• Solve: 2 x − 6x + 9 = 0
22. 22. Page 5 - Try It & Your Turn• Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0
23. 23. Page 5 - Try It & Your Turn• Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0x−3= 0 or x − 3 = 0
24. 24. Page 5 - Try It & Your Turn• Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0x−3= 0 or x − 3 = 0 +3 +3 +3 +3
25. 25. Page 5 - Try It & Your Turn• Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3
26. 26. Page 5 - Try It & Your Turn• Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
27. 27. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
28. 28. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( 2x − 7 ) ( 4x + 1) = 0 ( x − 3) ( x − 3) = 0x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
29. 29. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( 2x − 7 ) ( 4x + 1) = 0 ( x − 3) ( x − 3) = 0 2x − 7 = 0 or 4x + 1 = 0x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
30. 30. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( 2x − 7 ) ( 4x + 1) = 0 ( x − 3) ( x − 3) = 0 2x − 7 = 0 or 4x + 1 = 0x−3= 0 or x − 3 = 0 +7 +7 −1 −1 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
31. 31. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( 2x − 7 ) ( 4x + 1) = 0 ( x − 3) ( x − 3) = 0 2x − 7 = 0 or 4x + 1 = 0x−3= 0 or x − 3 = 0 +7 +7 −1 −1 +3 +3 +3 +3 2x = 7 or 4x = −1 x=3 or x=3 Answer: {3}
32. 32. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( 2x − 7 ) ( 4x + 1) = 0 ( x − 3) ( x − 3) = 0 2x − 7 = 0 or 4x + 1 = 0x−3= 0 or x − 3 = 0 +7 +7 −1 −1 +3 +3 +3 +3 2x = 7 or 4x = −1 x=3 or x=3 7 1 x= or x=− 2 4 Answer: {3}
33. 33. Page 5 - Try It & Your Turn• Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( 2x − 7 ) ( 4x + 1) = 0 ( x − 3) ( x − 3) = 0 2x − 7 = 0 or 4x + 1 = 0x−3= 0 or x − 3 = 0 +7 +7 −1 −1 +3 +3 +3 +3 2x = 7 or 4x = −1 x=3 or x=3 7 1 x= or x=− 2 4 Answer: {3} ⎧ 7 1 ⎫ Answer: ⎨ , − ⎬ ⎩ 2 4 ⎭
34. 34. Page 6 - Your Turn• Solve. 2 4a + 3a = 0
35. 35. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0
36. 36. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0
37. 37. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3
38. 38. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3 4a = −3
39. 39. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3 4a = −3 4 4
40. 40. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3 4a = −3 4 4 3 a=− 4
41. 41. Page 6 - Your Turn• Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3 4a = −3 4 4 ⎧ 3 ⎫ 3 Answer: ⎨0, − ⎬ a=− ⎩ 4 ⎭ 4
42. 42. Page 7 - Try It• Solve. 2 x − 25 = 0
43. 43. Page 7 - Try It• Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0
44. 44. Page 7 - Try It• Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0 x+5=0 or x−5=0
45. 45. Page 7 - Try It• Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0 x+5=0 or x−5=0 −5 −5 +5 +5
46. 46. Page 7 - Try It• Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0 x+5=0 or x−5=0 −5 −5 +5 +5 x = −5 or x=5
47. 47. Page 7 - Try It• Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0 x+5=0 or x−5=0 −5 −5 +5 +5 x = −5 or x=5 Answer: {−5, 5}
48. 48. Page 8 - Try It• Solve. 3 5x − 45x = 0
49. 49. Page 8 - Try It• Solve. 3 5x − 45x = 0 ( 2 ) 5x x − 9 = 0
50. 50. Page 8 - Try It• Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0
51. 51. Page 8 - Try It• Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0 5x = 0 or x+9=0 or x−9=0
52. 52. Page 8 - Try It• Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0 5x = 0 or x+9=0 or x−9=0 5 5 −9 −9 +9 +9
53. 53. Page 8 - Try It• Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0 5x = 0 or x+9=0 or x−9=0 5 5 −9 −9 +9 +9 x=0 or x = −9 or x=9
54. 54. Page 8 - Try It• Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0 5x = 0 or x+9=0 or x−9=0 5 5 −9 −9 +9 +9 x=0 or x = −9 or x=9 Answer: {0, −9, 9}
55. 55. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0
56. 56. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0)
57. 57. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0
58. 58. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0 y=0 or 2y − 1 = 0 or y+3= 0
59. 59. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0 y=0 or 2y − 1 = 0 or y+3= 0 +1 +1 −3 −3
60. 60. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0 y=0 or 2y − 1 = 0 or y+3= 0 +1 +1 −3 −3 2y = 1 or y = −3
61. 61. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0 y=0 or 2y − 1 = 0 or y+3= 0 +1 +1 −3 −3 2y = 1 or y = −3 2 2
62. 62. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0 y=0 or 2y − 1 = 0 or y+3= 0 +1 +1 −3 −3 2y = 1 or y = −3 2 2 y= 1 2
63. 63. Page 9 - Your Turn 3 2• Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0 y=0 or 2y − 1 = 0 or y+3= 0 +1 +1 −3 −3 2y = 1 or y = −3 2 2 ⎧ 1 ⎫ y= 1 2Answer: ⎨0, , −3⎬ ⎩ 2 ⎭
64. 64. Algebra Cruncher• Practice solving more Quadratic Equations at this Cool Math website.• Select the “Give me a Problem” button to try new problems.• Do your work in a notebook before entering your answer.• When you select “What’s the Answer?” your answer is erased and correct answer is displayed. Having your work in a notebook will allow you to compare your answer to the correct answer.• Keep working problems until you get 3 in a row correct.
65. 65. Fantastic Job!• You’ve ﬁnished reviewing Solving Quadratic Equations Part 1.• Exit and proceed to Part 2.