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Homework Help: When to complete the square?

  1. Oct 3, 2011 #1
    So i just have a general knowledge question. not rly hw related

    say u have a quadratic function or equation 4x2 – 2x – 5. Why would u have to complete the square in this situation? i know how to complete the square perfectly fine, but this was just bugging me.

    I know that if ur graphing u complete the square to get it in the form a(x-h)^2 +c which makes it easier to visualize, but in the case of a quadratic equation i dont see why u can't just make everything equal to x as is.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 3, 2011 #2


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    One completes the square to enable easy manual graphing and to help identify center, vertex, and other features of the graph.
  4. Oct 3, 2011 #3


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    Completing the square will also be used in maths later on with graphing circles, integration, inequality proofs etc.

    Also, completing the square makes graphing a quadratic easier when there are no real roots.
    If we solve [tex]x^2+2x+2=0[/tex] then the roots are [tex]x=-1\pm i[/tex] which doesn't really tell us anything about graphing it (other than it's completely above/below the x-axis), while [tex](x+1)^2+1[/tex] is much clearer.
  5. Oct 3, 2011 #4


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    Completing the square can be safer if you practice it, and it is good algebra practice to do it that way, if you have the time.
  6. Oct 3, 2011 #5


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    Please note that one of the forum rules is:
  7. Oct 3, 2011 #6
    oops :blushing: Sorry about that. Also thanks for those who replied. I pretty much get it now.
    Thanks for the help.
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