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Thread: Reversing the operation of completing the square

  1. #1
    Junior Member
    Join Date
    Jan 2012
    Posts
    158

    Reversing the operation of completing the square

    I have; 3x^2 + 18x + 15. I end up with 3(x+3)^2 - 12. I understand how I did this and don't need any help getting through to the end as shown.

    Now what I am asking help with is the reverse of the above.

    This is the final line of completing the square; 3(x + 1)^2 - 12

    If I expand the brackets and simplify I end up with; x + 3x - 11

    I have a graphics calculator and when I enter; 3(x + 1)^2 - 12 the y intercept when x=0 is - 9 and not - 11 as shown?

    My working out;

    3(x + 1)^2 - 12

    3(x + 1)(x + 1) - 12

    3(x^2 + x + x + 1) - 12

    3(x^2 + 2x + 1) - 12

    3x^2 + 6x + 3 - 36

    3x^2 + 6x - 33

    x^2 + 3x - 11

    If my graphic calculator is right could somebody please point out where I am going wrong!

    Thanks

  2. #2
    Elite Member
    Join Date
    Jun 2007
    Posts
    12,634
    Quote Originally Posted by Probability View Post
    I have; 3x^2 + 18x + 15. I end up with 3(x+3)^2 - 12. I understand how I did this and don't need any help getting through to the end as shown.

    Now what I am asking help with is the reverse of the above.

    This is the final line of completing the square; 3(x + 1)^2 - 12

    If I expand the brackets and simplify I end up with; x + 3x - 11

    I have a graphics calculator and when I enter; 3(x + 1)^2 - 12 the y intercept when x=0 is - 9 and not - 11 as shown?

    My working out;

    3(x + 1)^2 - 12

    3(x + 1)(x + 1) - 12

    3(x^2 + x + x + 1) - 12

    3(x^2 + 2x + 1) - 12

    3x^2 + 6x + 3 - 36 <<<<< This should be 3 * x^2 + 6 * x + 3 - 12

    = 3 * x^2 + 6 * x - 9

    Thus you have 'y-intercept' of '-9'



    3x^2 + 6x - 33

    x^2 + 3x - 11

    If my graphic calculator is right could somebody please point out where I am going wrong!

    Thanks
    .

    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Junior Member
    Join Date
    Jan 2012
    Posts
    158
    Quote Originally Posted by Subhotosh Khan View Post
    .

    Thanks for your help

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