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Math Help - Equation of a Parabola

  1. #1
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    Equation of a Parabola

    Find the equation of the parabola y = ax + bx + c that contains the points (1, -2), (2, 0), and (4, 22).

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  2. #2
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    Quote Originally Posted by bearej50 View Post
    Find the equation of the parabola y = ax + bx + c that contains the points (1, -2), (2, 0), and (4, 22).

    Plug in the points and you'll get three equations.

     a+b+c = -2

     4a+2b+c = 0

     16a+4b + c = 22

    You can solve this system of equations in a number of ways. I recommend setting up a matrix.

     \bigg(\begin{array}{ccc}<br />
1 & 1 & 1 \\<br />
4 & 2 & 1 \\<br />
16 & 4 & 1 \end{array}\bigg) \bigg( \begin{array}{ccc}<br />
a  \\<br />
b \\<br />
c  \end{array}\bigg) = \bigg(\begin{array}{ccc}<br />
-2  \\<br />
0 \\<br />
22  \end{array}  \bigg)

    So let's write that as  AX = B . We want to find x, hence:  X = BA^{-1}

    And you know how to calculate the inverse of a 3x3 matrix hopefully!  A^{-1} = \frac{adj(A)}{det(A)}
    Last edited by Mush; May 10th 2009 at 11:46 AM.
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  3. #3
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    I was taught a different way. Subtract the equations from one another.
    I got a = 13/5, b = -23/5, and c = 0. Is this right?
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  4. #4
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    Quote Originally Posted by bearej50 View Post
    I was taught a different way. Subtract the equations from one another.
    I got a = 13/5, b = -23/5, and c = 0. Is this right?
    Check yourself if it is right. If it satisfies the original equations it's right.

    Unfortunately yours are not. I get a = 3 ,b = -7, c = 2, and that is correct.
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