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Homework Help: Completing the Square with Coefficient on X^2

  1. Jul 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider all possible surfaces that can be formed from the variations of


    that is, find and describe all the different quadric surfaces you can make from this equation by using different signs on the degree 2 terms. For each one, find the standard form of the equation.

    I am having problems completing the square when the coefficient is negative.

    3. The attempt at a solution

    For the case where the y-coefficient is negative:

    (x^2 + 2x + 1) + (-4y^2 + 8y + _ ) + (z^2 +6z + 9) = -6 + 1 + _ + 9

    dividing by -4 gives: (y^2 - 2y + _ )

    Adding (b/2a)^2: (y^2 - 2y + 1)

    Condensing: (y - 1)^2

    Now, does the coefficient 4 come back as positive or negative, as in
    4(y - 1)^2 or -4(y - 1)^2

    Also, when adding to the other side of the equation, does the -4 multiply to the added quantity?

    Thanks for any help
  2. jcsd
  3. Jul 8, 2009 #2


    Staff: Mentor

    (-4y2 + 8y )
    = -(4y2 - 8y + __) + something

    You're going to add a positive number inside the parentheses, but you have really added a negative number, so to keep the expression in balance, add the positive of that negative number.

    Make sense?
  4. Jul 8, 2009 #3


    Staff: Mentor

    What else you should do to make your life simpler is to bring out the coefficient on the 2nd degree term so that you have
    -4(y2 - 2y + __) + something

    Just keep track of what you really added to the overall expression.
  5. Jul 8, 2009 #4
    Okay, thanks for helpin me out
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