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Math Help - Modeling With Quadratic Equations

  1. #1
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    Modeling With Quadratic Equations

    Okay, well I need a little help understanding this.

    Apparently from my homework I am given a parabola with 3 points, (0,0),(2,-2), and (3,4). I just need help understanding how to figure out the equation in standard form (y=ax^2+bx+c).

    So far all I have is:

    -2=a(1)^2+b(1)+c -> -2 = a+b+c
    -2=a(2)^2+b(2)+c -> -2 = 4a+2b+c
    4=a(3)^2+b(3)+c -> 4 =9a+3b+c

    All I really have to do is figure out what a,b, and c are and I can figure out the rest.

    Help please?

    Also, can you help explain how you came across doing it?

    Thanks
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  2. #2
    MHF Contributor
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    Quote Originally Posted by JosephLive93 View Post
    Okay, well I need a little help understanding this.

    Apparently from my homework I am given a parabola with 3 points, (0,0),(2,-2), and (3,4). I just need help understanding how to figure out the equation in standard form (y=ax^2+bx+c).

    The 3 given points are your 3 clues to find the 3 values a, b, c.

    So far all I have is:

    -2=a(1)^2+b(1)+c -> -2 = a+b+c........you need f(0)=0 here, or should that point have read (1,-2) ?
    -2=a(2)^2+b(2)+c -> -2 = 4a+2b+c
    4=a(3)^2+b(3)+c -> 4 =9a+3b+c

    All I really have to do is figure out what a,b, and c are and I can figure out the rest.

    Help please?

    Also, can you help explain how you came across doing it?

    Thanks
    f(0)=0\Rightarrow\ a(0)+b(0)+c=0\Rightarrow\ c=0

    f(2)=-2\Rightarrow\ a(2)^2+b(2)=-2

    f(3)=4\Rightarrow\ a(3)^2+b(3)=4

    With c accounted for, you only need solve the remaining pair of simultaneous equations
    for a and b.
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