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Solving quadratic equations part 1

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L
Lori Rapp

This document provides instruction on solving quadratic equations. It begins with an introduction explaining why quadratic equations are useful and includes a video example. It then defines quadratic equations and shows students how to identify the coefficients a, b, and c. The bulk of the document demonstrates two methods for solving quadratic equations: factoring and using the quadratic formula. It includes examples of each method and practice problems for students to work through. The goal is to teach students how to solve quadratic equations through factoring and using the formula.

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Solving Quadratic Equations PART 1
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!
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!
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.
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.
Page 2 - Try It 2 −3x − x − 5 = 0
Page 2 - Try It 2 • Find a, b, and c. −3x − x − 5 = 0
Page 2 - Try It 2 • Find a, b, and c. −3x − x − 5 = 0 a. -3 b. -1 c. -5
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
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
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.
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial.
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0.
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0 Solve each equation.
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation.
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation. x = −6 or x = −2
Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and 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}
Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0
Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0
Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0
Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3
Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3
Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
Page 5 - Try It & Your Turn • Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
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 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
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 = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
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 = 0 x−3= 0 or x − 3 = 0 +7 +7 −1 −1 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
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 = 0 x−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}
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 = 0 x−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}
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 = 0 x−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 ⎭
Page 6 - Your Turn • Solve. 2 4a + 3a = 0
Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0
Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0
Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3
Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3 4a = −3
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
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
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
Page 7 - Try It • Solve. 2 x − 25 = 0
Page 7 - Try It • Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0
Page 7 - Try It • Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0 x+5=0 or x−5=0
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
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
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}
Page 8 - Try It • Solve. 3 5x − 45x = 0
Page 8 - Try It • Solve. 3 5x − 45x = 0 ( 2 ) 5x x − 9 = 0
Page 8 - Try It • Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0
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
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
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
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}
Page 9 - Your Turn 3 2 • Solve. 2y + 5y − 3y = 0
Page 9 - Your Turn 3 2 • Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0)
Page 9 - Your Turn 3 2 • Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0 ) y ( 2y − 1) ( y + 3) = 0
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
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
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
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
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
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 2 Answer: ⎨0, , −3⎬ ⎩ 2 ⎭
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.
Fantastic Job! • You’ve finished reviewing Solving Quadratic Equations Part 1. • Exit and proceed to Part 2.

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Solving quadratic equations part 1

  • 1. Solving Quadratic Equations PART 1
  • 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. 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. 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. 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. Page 2 - Try It 2 −3x − x − 5 = 0
  • 7. Page 2 - Try It 2 • Find a, b, and c. −3x − x − 5 = 0
  • 8. Page 2 - Try It 2 • Find a, b, and c. −3x − x − 5 = 0 a. -3 b. -1 c. -5
  • 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. 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. 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. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0
  • 13. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial.
  • 14. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0
  • 15. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0.
  • 16. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0
  • 17. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0 Solve each equation.
  • 18. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation.
  • 19. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and set equal to 0. x+6=0 or x+2=0 Solve each −6 −6 −2 −2 equation. x = −6 or x = −2
  • 20. Page 4 - Try It • Solve. 2 x + 8x + 12 = 0 Factor the trinomial. ( x + 6 )( x + 2 ) = 0 Split the factors and 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. Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0
  • 22. Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0
  • 23. Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0
  • 24. Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3
  • 25. Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3
  • 26. Page 5 - Try It & Your Turn • Solve: 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
  • 27. Page 5 - Try It & Your Turn • Solve: 2 8x − 26x − 7 = 0 2 x − 6x + 9 = 0 ( x − 3) ( x − 3) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
  • 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) = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
  • 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 = 0 x−3= 0 or x − 3 = 0 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
  • 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 = 0 x−3= 0 or x − 3 = 0 +7 +7 −1 −1 +3 +3 +3 +3 x=3 or x=3 Answer: {3}
  • 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 = 0 x−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. 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 = 0 x−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. 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 = 0 x−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. Page 6 - Your Turn • Solve. 2 4a + 3a = 0
  • 35. Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0
  • 36. Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0
  • 37. Page 6 - Your Turn • Solve. 2 4a + 3a = 0 a ( 4a + 3) = 0 a=0 or 4a + 3 = 0 −3 −3
  • 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. 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. 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. 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. Page 7 - Try It • Solve. 2 x − 25 = 0
  • 43. Page 7 - Try It • Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0
  • 44. Page 7 - Try It • Solve. 2 x − 25 = 0 ( x + 5 )( x − 5 ) = 0 x+5=0 or x−5=0
  • 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. 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. 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. Page 8 - Try It • Solve. 3 5x − 45x = 0
  • 49. Page 8 - Try It • Solve. 3 5x − 45x = 0 ( 2 ) 5x x − 9 = 0
  • 50. Page 8 - Try It • Solve. 3 5x − 45x = 0 ( 2 5x x − 9 = 0 ) 5x ( x + 9 ) ( x − 9 ) = 0
  • 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. 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. 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. 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. Page 9 - Your Turn 3 2 • Solve. 2y + 5y − 3y = 0
  • 56. Page 9 - Your Turn 3 2 • Solve. 2y + 5y − 3y = 0 ( 2 y 2y + 5y − 3 = 0)
  • 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. 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. 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. 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. 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. 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. 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 2 Answer: ⎨0, , −3⎬ ⎩ 2 ⎭
  • 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. Fantastic Job! • You’ve finished reviewing Solving Quadratic Equations Part 1. • Exit and proceed to Part 2.

Editor's Notes