Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

1,665

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
1,665
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
0
0
Likes
0
Embeds 0
No embeds

No notes for slide
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• Transcript

• 1. Solving Quadratic Equations PART 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. Page 1 - Finish it• Solve. 2 x − 3x − 18 = 0
• 4. Page 1 - Finish it• Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0
• 5. Page 1 - Finish it• Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0
• 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. 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. 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. Page 1 - Your Turn 2• Solve. x + 7x = 170
• 10. Page 1 - Your Turn 2• Solve. x + 7x = 170 −170 −170
• 11. Page 1 - Your Turn 2• Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0
• 12. Page 1 - Your Turn 2• Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0
• 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. 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. 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. 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. Page 2 - Finish it• Solve. 2 2x − 5x − 3 = 0
• 18. Page 2 - Finish it• Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0
• 19. Page 2 - Finish it• Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0
• 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. 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. 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. 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. 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. Page 2 - Your Turn• Solve. 2 11x + 6 − 10x = 0
• 26. Page 2 - Your Turn• Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1
• 27. Page 2 - Your Turn• Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0
• 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. 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. 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. 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. 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. 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. 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. 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. Page 3 - Your Turn 3• Solve. −16x = −4x
• 37. Page 3 - Your Turn 3• Solve. −16x = −4x +4x 3 +4x 3
• 38. Page 3 - Your Turn 3• Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0
• 39. Page 3 - Your Turn 3• Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0)
• 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. 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. 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. 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. 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. 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. Fantastic Job!• You’ve ﬁnished reviewing Solving Quadratic Equations Part 2.• Exit and proceed to the Homework Assignment.