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Math Help - [SOLVED] Convert parabola to standard form

  1. #1
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    [SOLVED] Convert parabola to standard form

    2y^2 + x - 16y + 26 = 0

    - x = 2y^2 - 16y + 26 (Moved x to the other side)

    - x = 2(y^2 - 8y + 13) (Factored out 2)

    x = - 2(y^2 - 8y + 13) (Divide sides by -1)

    x + 26 = - 2(y^2 - 8y) (Move 13 to the left side, but first multiply it by -2, resulting in -26, therefore add 26 to each side)

    x + 26 + 32 = - 2(y^2 - 8y + 16) (Complete the square on the right side, add 16 to both sides, but it has to be multiplied by -2 before I bring it to the left side, which results in -32, therefore add 32 to the left side.

    x + 58 = - 2(y-4)^2

    x = - 2(y-4)^2 - 58

    This answer is wrong, where did I go wrong?
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  2. #2
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    Quote Originally Posted by Phire View Post
    2y^2 + x - 16y + 26 = 0

    - x = 2y^2 - 16y + 26 (Moved x to the other side)

    - x = 2(y^2 - 8y + 13) (Factored out 2)

    x = - 2(y^2 - 8y + 13) (Divide sides by -1)

    x + 26 = - 2(y^2 - 8y) (Move 13 to the left side, but first multiply it by -2, resulting in -26, therefore add 26 to each side)

    x + 26 + 32 = - 2(y^2 - 8y + 16) (Complete the square on the right side, add 16 to both sides, but it has to be multiplied by -2 before I bring it to the left side, which results in -32, therefore add 32 to the left side.

    x + 58 = - 2(y-4)^2

    x = - 2(y-4)^2 - 58

    This answer is wrong, where did I go wrong?
    The red plus sign should be a minus sign. Expand the right hand side and you'll see why (you have essentially substracted 32 from the right hand side).
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    The red plus sign should be a minus sign. Expand the right hand side and you'll see why (you have essentially substracted 32 from the right hand side).
    I'm still confused, if I expand:

    - 2(y^2 - 8y + 16)

    I get:

    2y^2 + 16y - 32
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  4. #4
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    Quote Originally Posted by Phire View Post
    x + 26 + 32 =

    ...

    2y^2 + 16y - 32
    You are adding 32 to the left side, but subtracting 32 from the right. This is not a valid step.
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  5. #5
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    Wow, I confused the heck out of myself, but I understand now. Thanks.
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