Upcoming SlideShare
×

# Module 10 Topic 4 solving quadratic equations part 2

5,533 views

Published on

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
5,533
On SlideShare
0
From Embeds
0
Number of Embeds
4,607
Actions
Shares
0
0
0
Likes
0
Embeds 0
No embeds

No notes for slide

• ### Module 10 Topic 4 solving quadratic equations part 2

1. 1. Solving Quadratic Equations Module 10 - Topic 4 PART 2
2. 2. Solving Quadratic Equations when they do NOT equal ZERO • So far all the quadratic equations we’ve solve have been equal to zero but not all are so nice. If they don’t equal zero, make them equal to zero! • View this Cool Math website to how to solve Quadratic Equations when the original equation is not equal to 0. • There are 3 pages to view. • Complete the Your Turn problems in your notebook and check your answers on the next slide.
3. 3. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0
4. 4. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0
5. 5. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0
6. 6. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6
7. 7. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6 x = −3 or x=6
8. 8. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6 x = −3 or x=6 Answer: {−3, 6}
9. 9. Page 1 - Your Turn 2 • Solve. x + 7x = 170
10. 10. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170
11. 11. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0
12. 12. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0
13. 13. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0
14. 14. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10
15. 15. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10 x = −17 or x = 10
16. 16. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10 x = −17 or x = 10 Answer: {−17,10}
17. 17. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0
18. 18. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0
19. 19. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0
20. 20. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3
21. 21. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3
22. 22. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3 2 2
23. 23. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3 2 2 x = − 12
24. 24. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3 2 2 x = − 12  1  Answer: − , 3  2 
25. 25. Page 2 - Your Turn • Solve. 2 11x + 6 − 10x = 0
26. 26. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1
27. 27. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0
28. 28. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0
29. 29. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0
30. 30. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0
31. 31. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3
32. 32. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3
33. 33. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3 5 5 2 2
34. 34. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3 5 5 2 2 x = −25 or x= 3 2
35. 35. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3 5 5 2 2  2 3 Answer: − ,  x = −25 or x= 3 2  5 2
36. 36. Page 3 - Your Turn 3 • Solve. −16x = −4x
37. 37. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3
38. 38. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0
39. 39. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0)
40. 40. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0 ) 4x ( x + 2 ) ( x − 2 ) = 0
41. 41. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0 ) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0
42. 42. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0 4 4 −2 −2 +2 +2
43. 43. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0 4 4 −2 −2 +2 +2 x=0 or x = −2 or x=2
44. 44. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0 4 4 −2 −2 +2 +2 x=0 or x = −2 or x=2 Answer: {0, −2, 2}
45. 45. Do you want to Play a GAME? • Check your knowledge on solving Quadratic Equations by playing Jeopardy. Ok, technically it’s called Challenge Board but it’s the same idea! • You have the option to play alone or against a friend or maybe a family member! • You could even arrange a time with a classmate to meet on Pronto to play. Try the App Share feature to see the same game board! • Finding the x-intercepts is the same as solving!
46. 46. Fantastic Job! • You’ve ﬁnished reviewing Solving Quadratic Equations Part 2. • Exit and proceed to the Mastery Assignment.