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Homework Help: Simple linear algebra refresher?

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Given the three x-values {-1,1,2} and the corresponding y-values {-1,1,8}, write down the three equations that define the quadratic polynomial that interpolates this data.

    I have completely forgot how to do this.

    Thanks


    2. Relevant equations

    IDK y=mx+b



    3. The attempt at a solution

    none, I already have taken calculus 1-3 and de, and I cannot remember how to do this :(
     
  2. jcsd
  3. Feb 15, 2010 #2

    Hurkyl

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    Before worrying about how to do the question, try first stating what the question is, symbolically.
     
  4. Feb 15, 2010 #3
    Like I said I don't remember anything my brain is fried for some reason.

    Looking at the data I just know that they are points
    (-1,-1) (1,1) (2,8)

    I got

    -1=a-b+c
    1=a+b+c
    8=4a+2b+c

    ???
     
    Last edited: Feb 15, 2010
  5. Feb 15, 2010 #4

    Hurkyl

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    From the latest post, I suspect you've remembered a lot more than you let on -- just to double check, can you say what a, b, and c are, and how they relate to the quadratic interpolating polynomial you're trying to find?



    So anyways -- you've reduced the problem to "How do I solve a system of three linear equations in three unknown variables?" right? And there's nothing else to it?
     
  6. Feb 15, 2010 #5
    :rofl: I solve for a, b, c using the solver I got 6, 1, -6

    So I guess the quadratic polynomial that interpolates the data is f(x)= 6x^2+Y-6, correct?


    In this part, is he asking for the 3X3 matrix of the 3 equations?
    a=[1 -1 1; 1 1 1; 2 2 1] b=[-1 1 8]
    where
    a*X=b
     
  7. Feb 15, 2010 #6

    Mark44

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    Hurkyl's asking you what a, b, and c represent (not their values) in terms of the interpolating quadratic.
     
  8. Feb 16, 2010 #7
    the values in which the interpolation will take place?
     
  9. Feb 16, 2010 #8

    Mark44

    Staff: Mentor

    No - what is the interpolating polynomial you are using?
     
  10. Feb 16, 2010 #9
    Is this one f(x)= 6x^2+Y-6
     
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