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Activating Strategy

Activating Strategy. Sitback , watch, and be observant! Then write down something we haven’t discussed that was in the video. Topic 2: Solving Quadratic Equations. Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root?

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Activating Strategy

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  1. Activating Strategy Sitback, watch, and be observant! Then write down something we haven’t discussed that was in the video.

  2. Topic 2: Solving Quadratic Equations Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6

  3. Vocab Polynomial ~ any expression with more than one term Monomial ~ an expression with one term Binomial ~ an expression with two terms Trinomial ~ an expression with three terms

  4. Factoring • A process used to rewrite a polynomial as a product of other polynomials having equal or lesser degree. • Ex) x2 + 8x + 15 = (x + 3)(x + 5) • Notice if you FOIL (x + 3)(x + 5) you get x2 + 8x + 15 • FOILING and FACTORING are opposites

  5. Factoring x2 + bx + c(Reverse FOIL Method) • x2 + 11x + 30 • x2 – 12x – 28

  6. Your Turn… Factor the following trinomials. If it cannot be factored answer “Not Factorable.” x2 + 5x + 4 x2 + 13x + 40 x2– 4x + 3 x2– 16x + 50

  7. Your Turn… Factor the following trinomials. If it cannot be factored answer “Not Factorable.” x2 + 9x + 14 x2– 8x + 12 x2– 4x + 6 x2+ 3x – 10

  8. Solving x2 + bx + c(can’t isolate “x”) • Zero Product Property • If A·B = 0, then A = 0 or B = 0 • Example: x2 + 3x – 18 = 0 • In topic 1, what would have been in the “0” place? • What does that tell us about the solutions we just found? • What quadratic form does solving relate to? • This is why we call it finding the zeros!!

  9. Your Turn… Solve the following trinomials using the zero product property. x2 + 4x + 3 = 0 x2 + 13x + 30 = 0 x2– 5x – 6 = 0 x2– 2x + 1 = 0

  10. Factoring ax2 + bx + c(Reverse FOIL Method or Box Method) • 3x2 - 17x + 10 • 4x2 – 4x – 3

  11. Your Turn… Factor the following trinomials. If it cannot be factored answer “Not Factorable.” 2x2 + 7x + 3 5x2 – 7x + 2 3x2 + 17x + 10 8x2 + 18x + 9

  12. Solving ax2 + bx + c(can’t isolate “x”) • Zero Product Property • If A·B = 0, then A = 0 or B = 0 • Example: 3x2 + x – 2 = 0 • In topic 1, what would have been in the “0” place? • What does that tell us about the solutions we just found? • What quadratic form does solving relate to? • This is why we call it finding the zeros!!

  13. Your Turn… Solve the following trinomials using the zero product property. 7x2 + 10x + 3 = 0 5x2+ 7x + 2 = 0 8x2 – 22x + 5 = 0 2x2– 5x – 25 = 0

  14. Summarizing Strategy When solving a quadratic equation, describe what you are specifically finding on the quadratics graph.

  15. Practice 5.2 Practice B WS #1 – 12: just factor #13 – 24: set = 0 and solve

  16. Activating Strategy • Solve: x2 + 3x – 10 = 0 • Solve: 3x2 – x – 4 = 0

  17. Topic 2: Solving Quadratic Equations Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6

  18. Factoring a2 – b2(Reverse FOIL Method or Difference of 2 Squares) • x2 – 9 • 25x2 – 36 VERY IMPORTANT ~ ONLY WORKS WITH SUBTRACTION…NOT ADDITION!

  19. Your Turn… Factor the following binomials. If it cannot be factored write “Not Factorable.” x2 – 16 4x2 – 49 49x2 + 4 16x2– 9

  20. Solving a2 – b2 • Zero Product Property • If A·B = 0, then A = 0 or B = 0 • Example: 4x2 – 25 = 0 • In topic 1, what would have been in the “0” place? • What does that tell us about the solutions we just found? • What quadratic form does solving relate to? • This is why we call it finding the zeros!!

  21. Your Turn… Solve the following binomials using the zero product property. x2 – 9 = 0 4x2 – 81 = 0 49x2 – 16 = 0 16x2– 1 = 0

  22. Let’s Start Over…and make things easier! Before using any of the methods we have learned about so far we should first check for a GCF from now on! GRAPHIC ORGANIZER

  23. Factoring with a GCF(Factor Tree) • 5x2 – 20 • 6x2 + 15x + 9

  24. Solving with a GCF(Factor Tree) • 2x2 + 8x = 0 • 4x2 + 4x + 4 = 0

  25. Factoring with a GCF(Factor Tree) Factor/Solve/Both? 2x2 – 17x + 45 = 3x – 5

  26. Your Turn… Solve the following using the zero product property. 3x – 6 = x2 – 10 x2 + 19x + 88 = 0 x2 + 9x = -20

  27. Summarizing Strategy Explain the mistake shown below. x2+ 4x + 3 = 8 (x + 3)(x + 1) = 8 x + 3 = 8 or x + 1 = 8 x = 5 or x = 7

  28. Practice 5.2 Practice B WS #25 – 33: just factor #34 – 45: set = 0 and solve

  29. Activating Strategy Solve: -4x2 + 36 = 0

  30. Topic 2: Solving Quadratic Equations Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6

  31. Vocab A number r is a square root of a number s if r2 = s

  32. Simplfying Radicals • No radicand has a perfect square factor other than one. • No radical in the denominator.

  33. Examples

  34. Classwork 2.2 Radicals Practice WS

  35. Solving by Square Root (3)(3) = 9 (-3)(-3) = 9 Very Important: If you take a square root when solving, you must use +/-

  36. Solving by Square Root(can isolate “x”) 1/3(x + 5)2 = 7 Get (something)2 by itself first! • 2x2 + 1 = 17

  37. Your Turn… Solve by taking the square root. 2(x – 3)2 = 8 x = 1 and 5 -3(x +2)2 = -18 x = -2  6 ¼(x – 8)2 = 7 x = 8  27

  38. Application • The height, h, of an object dropped from an initial height, h0, is modeled by the equation: h = -16t2 +h0 where t is the number of seconds after the object has been dropped. • An object is dropped from the top of a 100 foot building. • How high is it after 1 second? • How long until the object hits the ground?

  39. Summarizing Strategy How do you know when you should solve by factoring or solve by taking the square root?

  40. Practice Pg. 267 #4 – 17 all

  41. Activating Strategy • Solve: 2x2 – 8x – 10 = 0 • Solve: 4x2 + 11 = 35

  42. Topic 2: Solving Quadratic Equations Algebra II: Unit 2 How are quadratic equations solved by factoring, quadratic formula, taking the square root? Book: 5.2, 5.3, 5.6

  43. Remember Solutions are where the graph crosses the x-axis. These are called zeros or roots.

  44. What are the 2 methods of solving a quadratic equation that we have learned so far? Factoring Square rooting Completing the square Quadratic Formula

  45. Quadratic Formula Ever hear this? A 3rd method of solving ANY quadratic equation is by using the quadratic formula. If ax2 + bx + c = 0 then…

  46. Solving using the Quadratic Formula Steps Get into standard form and set = 0 Fill a, b, and c into the quadratic formula 2x2 + x = 5

  47. Solving using the Quadratic Formula Steps Get into standard form and set = 0 Fill a, b, and c into the quadratic formula x2 - x = 5x - 9

  48. Solving using the Quadratic Formula Steps Get into standard form and set = 0 Fill a, b, and c into the quadratic formula 10x2 + 8x – 1 = 0

  49. Discriminant • The expression under the radical sign, b2 – 4ac • Can be used to determine the equation’s # of solutions and type of solutions

  50. Discriminant

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