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Math Help - Writing a quadratic function using a table of values

  1. #1
    Member wiseguy's Avatar
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    Writing a quadratic function using a table of values

    "A quadratic function f contains these points.
    x y
    3 36.7
    5 27.5
    7 20.7
    9 16.3
    11 14.3

    Find the particular equation for f(x) as a function of x."



    Here is my response:
    ax^2+bx+c
    36.7=a(3)^2+b(3)+c
    36.7=9a+3b+c
    36.7-9a-3b=c

    27.5=a(5)^2+b(5)+(36.7-9a-3b)
    -9.2=16a+2b
    (-9.2-16a)/2=b

    20.7=a(7)^2+((-9.2-16a)/2)7+(36.7-9a-3((-9.2-16a)/2))
    20.7=49a+(-4.6-8a)7+(6.7-9a-3(-4.6-8a))
    20.7=49a-32.2-56a+6.7-9a+13.8+24a
    20.7=-11.7+8a
    32.4=8a
    a=4.05

    16.3=4.05(9)^2+((-9.2-16(4.05))/2)(9)+(36.7-9(4.05)-3((-9.2-
    16(4.05))/2))
    16.3=4.05(9)^2-37(9)+111.25



    Unfortunately, after double checking it into the calculator (using quadratic regression), the real equation is 0.3x^2+-7x+55 ...I'm at a bit of a loss.


    Any help would be greatly appreciated
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    I also get y = 0.3x^2 - 7x + 55 using the least squares regression model. Do you know this model?
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  3. #3
    Member wiseguy's Avatar
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    No I do not, but I would love to find out...
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  4. #4
    Master Of Puppets
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    Check this example. Curve Fitting, Part 1

    Using technology will be easier though, I found your equation very easily using ms-excel.
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  5. #5
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    I think you're given that those are points on a quadratic equation, ie this is not an estimation. just assume the form ax^2 + bx + c = y and make 3 equations using any 3 y/x relationships you know and solve the system of 3 unknowns for a, b, and c.

    I ran an rref on a matrix like so and got the right answer:
    [3^2, 3, 1, 36.7]
    [5^2, 5, 1, 27.5]
    [7^2, 7, 1, 20.7]
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  6. #6
    Member wiseguy's Avatar
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    36.7=a(3)^2+b(3)+c
    27.5=a(5)^2+b(5)+c
    20.7=a(7)^2+b(7)+c

    36.7-9a-3b=27.5-25a-5b
    -27.5+25a+5b=-20.7+49a+7b

    36.7-9a-3b=-20.7+49a+7b
    57.4-58a=10b
    5.74-5.8a=b

    36.7-9a-3(5.74-5.8a)=-20.7+49a+7(5.74-5.8a)
    36.7-9a-17.22+17.4a=-20.7+49a+40.18-40.6a
    80.36=-9a
    a=-8.928888888

    b=-46.04755555


    Still not the correct answer... someone please help!
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