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Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. Chapter 10 Lesson 10-5. Introduction.

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Solving Quadratic Equations by Factoring

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  1. Solving Quadratic Equations by Factoring Chapter 10 Lesson 10-5

  2. Introduction This stAIR is designed for Ms. Goghar’s Grade 9 Algebra 1 class. You are expected to follow directions on each slide and navigate through this powerpoint carefully. Your goal is to understand the concept of solving quadratic equations and its relation to the roots (zeros) of quadratic functions and to learn how to solve quadratic equations by factoring.

  3. Objective: To master the skill of solving quadratic equations by factoring

  4. Required Materials: Pencil, Paper, and eraser TI-84 (optional)

  5. The next 6 slides are Warm-Up Review Problems. Being able to successfully solve these problems will ensure that you are ready to work on this lesson.

  6. Lesson Warm-Up #1 Solve this equation for n: What does n equal? -1 2

  7. You Are Right!!

  8. Try Again!!Study this Example: First, you should subtract 6 from both sides. Now, what should the next step be? What does n equal? -1 2

  9. Try Again!! First, you should subtract 6 from both sides. Now you need to divide both sides by 4. What does n equal? -1 2

  10. Try Again!! First, you should subtract 6 from both sides Then, divide both sides by 4 What does n equal? -1 2

  11. Lesson Warm-Up #2 Solve for a: What does a equal? 104 -40

  12. You Are Right!!! Solve for a:

  13. Try Again!!Study this Example: NOW: Solve for a: Step 1: Add 9 on both sides So, Think: What is the 2nd Step you need to do to solve for a? What does a equal? -40 104

  14. Try Again! Solve for a: Step 1: Add 9 on both sides Step 2: Multiply 8 to both sides What does a equal? -40 104

  15. Lesson Warm-Up #3 Factor the expression completely: What is the Complete Factored form?

  16. You Are Right!!! Factor the expression:

  17. Try Again!!! Factor the expression completely: Step 1: Factor out the GCF. In this case, GCF = 2. Step 2: You need to factor Note: Factoring Difference of Perfect Squares: What is the Complete Factored form?

  18. Try Again!!! Factor the expression completely: Step 1: Factor out the GCF. In this case, GCF = 2. Step 2: Factor So now, what is the Complete Factored form?

  19. Lesson Warm-Up #4 Factor the expression: Is it: OR

  20. You Are Right!!! Factor the expression: This expression cannot be factored. Therefore, it is

  21. Try Again!!! Notes: Steps to Factor Polynomials: I Un-DISTRIBUTE GCF II Un-FOIL a2 - b2 III Un-FOIL ax2 + bx + c IV Polynomials that cannot be factored are PRIME Hint: Is it possible to factor the given expression? Does it follow any of the factoring rules listed above? Back to Lesson Warm-Up #4

  22. Lesson Warm-Up #5 Factor the expression completely: What is the expression in factored form?

  23. You Are Right!!! Factor the expression completely: Expression in Factored Form:

  24. Study the Notes Below: Steps to Factor Polynomials: I Un-DISTRIBUTE GCF II Un-FOIL a2 - b2 III Un-FOIL ax2 + bx + c IV Polynomials that cannot be factored are PRIME Factor completely: Try Again!!

  25. Try Again!! Factor the expression completely: Step 1: (2c+___)(c+___) You need to think of factors of 14 that will work. Possibilities: 1 and 14; 2 and 7 Remember to check for the middle term when you FOIL. What is the expression in factored form?

  26. Lesson Warm-Up #6 Factor the expression completely: What is the expression in factored form?

  27. You Are Right!!! Factor the expression:

  28. Try Again!!! Study the Notes Below: Steps to Factor Polynomials: I Un-DISTRIBUTE GCF II Un-FOIL a2 - b2 III Un-FOIL ax2 + bx + c IV Polynomials that cannot be factored are PRIME Factor completely:

  29. Try Again!!! Factor the expression completely: Step 1: (3p+___)(p+___) Think: What Factors of 20 will give you the correct middle term? What is the expression in factored form?

  30. Watch this video to get a sense of what we are going to do for the rest of this lesson:You need to return and continue working on this project after watching the video.

  31. Zero-Product Property For every real number a and b, if ab = 0, then a = 0 or b = 0. Example: If , then x + 2 = 0 or x + 3 = 0

  32. Checking Your Understanding #1: If x = 0, then You have 5 seconds to think before the answer appears…

  33. Checking Your Understanding #2: If y= 0, then You have 5 seconds to think before the answer appears…

  34. What should you do on the “Example” pages: Study the Example Question carefully and think about how you may want to solve it The worked out solution(s) and the final answer of the example will appear after a few seconds Study every step of the solution and the answer carefully so you will be able to solve similar problems later on When you are ready to continue, navigate to the next slide.

  35. What should you do on the “You Try” pages: Study the “You Try” Question carefully and think about how you may want to solve it Solve the problem on the paper that you have with you The worked out solution(s) and the final answer of the problem will appear after 10-15 seconds Check your work (step-by-step) with the worked out solution and final answer If you made mistakes in solving the problem on your paper, you should correct them When you are ready to continue, navigate to the next slide.

  36. Example 1: Using the Zero-Product Property, Solve:

  37. Example 1 continues: Check your Solutions:

  38. You Try #1: Using the Zero-Product Property, Solve:

  39. You Try #2: Using the Zero-Product Property, Solve:

  40. You Try #3: Using the Zero-Product Property, Solve:

  41. Quick Check A. Solve: B. C.

  42. Yippee!YOU GOT IT! Solve:

  43. Oops!You need to review the Example and You Try Problems… Back to Examples

  44. Example 2: Solve by Factoring:

  45. You Try: Solve by Factoring:

  46. Quick Check A. Solve: B. C.

  47. Yippee!YOU GOT IT! Solve:

  48. Oops!You need to review the Example and You Try Problems… Back to Examples

  49. Example 3: Solve by Factoring:

  50. You Try: Solve by Factoring:

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