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Math Help - Algebra

  1. #1
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    Algebra

    fit a quadratic polynomial to the points (1,4),(3,8),(-2,8) by writing the general equation, setting up and solving of 3 linear equations.

    how to solve using row reduce method?
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  2. #2
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    Hello, trythis!

    Fit a quadratic polynomial to the points (1,4), (3,8), (-2,8)
    by writing the general equation, setting up and solving of 3 linear equations.

    how to solve using row-reduce method?

    The general quadatic is: . f(x) \:=\:ax^2+bx+c


    Those three points must satisfy the equation, so we have:

    . . \begin{array}{ccccc}f(1) = 4 & & a + b + c &=& 4 \\ f(3)=8 & & 9a + 3b + c &=& 8 \\ f(\text{-}2) = 8 & & 4a - 2b + c &=&8 \end{array}

    Then we have the augmented matrix: . \left[\begin{array}{ccc|c}1 & 1 & 1 & 4 \\ 9 & 3 & 1 & 8 \\ 4 & \text{-}2 & 1 & 8 \end{array}\right]


    . . and I assume you know how to row-reduce it . . .

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  3. #3
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    how u got this equation,plse explain?

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  4. #4
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    Quote Originally Posted by mathseek View Post
    This is how he did it

    For the point (1,4). if x=1 and y=4 then f(x)=ax^{2}+bx+c \Rightarrow f(1)=a(1)^{2}+b(1)+c  \Rightarrow a+b+c=4

    For (3,8) f(x)=ax^{2}+bx+c \Rightarrow f(3)=a(3)^{2}+b(3)+c  \Rightarrow 9a+3b+c=8

    For (-2,8) f(x)=ax^{2}+bx+c \Rightarrow f(-2)=a(-2)^{2}+b(-2)+c  \Rightarrow 4a-2b+c=8

    Just plug in the values that you were given for each quadratic equation.
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