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    Presentation1 Presentation1 Presentation Transcript

    • Completing the Square
    • Practice factoring the following using the algebra tiles above:
      x2+ 5x + 6
      x2+ 4x + 4
      x2+ 6x + 9
      x2+ 8x + 16
      click on to check your work…
    • #1) x2+ 5x + 6
    • #1) x2+ 5x + 6
    • #1) x2+ 5x + 6
      (x + 3) (x + 2)
    • x2 + 4x + 4
    • #2) x2+ 4x + 4
    • #2) x2+ 4x + 4
      (x + 2)(x + 2) = (x + 2)2
    • #3) x2+ 6x + 9
    • #3) x2+ 6x + 9
    • #3) x2+ 6x + 9
      (x + 3)(x + 3) = (x + 3)2
    • #4) x2+ 8x + 16
    • #4) x2+ 8x + 16
    • #4) x2+ 8x + 16
      (x + 4)(x + 4) = (x + 4)2
    • What do #2, 3 & 4 have in common when you built them?  
    • What do #2, 3 & 4 have in common when you built them?  
      They all made squares!!!
    • Try factoring 4x2+ 8x + 4.  What do you notice?
    • Try factoring 4x2+ 8x + 4.  What do you notice?
    • Try factoring 4x2+ 8x + 4.  What do you notice?
      It’s still a square!!
      (2x + 2)2
    • All of the above examples are considered perfect square trinomials.  Being able to rewrite a trinomial in "perfect square" form allows you to solve for it using the square root method instead of the quadratic formula.  
    • Solve each of the following equations:A.  x2+ 4x + 1 = 0 B.  (x + 2)2= 3
    • Solve each of the following equations:A.  x2+ 4x + 1 = 0 B.  (x + 2)2= 3
    • Solve each of the following equations:A.  x2+ 4x + 1 = 0 B.  (x + 2)2= 3
      You ended up getting the same answer!
    • Which method do you think was more straight forward? A or B?
    • Build a square (the best you can) to factor x2 + 4x + 1
    • Build a square (the best you can) to factor x2 + 4x + 1
    • What do you need to “add” to complete your square?
    • You needed to borrow 3 tiles…
    • How will you write this algebraically?
    • x2+ 4x + 1 + 3 – 3x2 + 4x + 4– 3
    • How will you now write this in “factored” form?
      x2 + 4x + 4 – 3
    • How will you now write this in “factored” form?
      x2 + 4x + 4 – 3 =
      (x +2)2 - 3
    • Practice completing the square on the following expressions:
      x2 + 6x + 5
      x2 + 8x + 5
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = x2 + 6x + 5 + 4 - 4
      x2 + 8x + 5
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = x2 + 6x + 5 + 4 – 4
      = (x + 3)2 - 4
      x2 + 8x + 5
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = x2 + 8x + 5 + 11 - 11
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = x2 + 8x + 5 + 11 – 11
      = (x + 4)2 - 11
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = (x + 4)2 - 11
      4x2+ 8x + 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = (x + 4)2 - 11
      4x2+ 8x + 1 = 4x2 + 4x + 1 + 1 – 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = (x + 4)2 - 11
      4x2+ 8x + 1 = 4x2 + 4x + 1 + 1 – 1
      = (2x + 2)2 – 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = (x + 4)2 - 11
      4x2+ 8x + 1 = (2x + 2)2 – 1
    • Practice completing the square on the following expressions:
      x2 + 6x + 5 = (x + 3)2 - 4
      x2 + 8x + 5 = (x + 4)2 - 11
      4x2+ 8x + 1 = (2x + 2)2 – 1
    • What did you notice about all the problems in this lesson?
    • What did you notice about all the problems in this lesson?
      Everything was positive.
    • On the wall wisher below, how would this process change when given negative values in your expression? Be sure to put your name on your note to get credit!