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Thread: Formula of Parabola = ??

  1. #1
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    Formula of Parabola = ??

    How can you find in a simple way the formula of Parabola that passes
    through the point $\displaystyle p(2,1)$ and passes through the points of intersection
    of functions $\displaystyle y = x^2 + 3x + 7$ & $\displaystyle y = -2x^2 + x + 10$
    Last edited by razemsoft21; Apr 29th 2009 at 07:00 AM.
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  2. #2
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    Quote Originally Posted by razemsoft21 View Post
    How can you find in a simple way the formula of Parabola that passes
    through the point $\displaystyle p(2,1)$ and passes through the points of intersection
    of functions $\displaystyle y = x^2 + 3x + 7$ & $\displaystyle y = -2x + x + 9$
    Step 1: Solve the following equations simultaneously:

    $\displaystyle y = x^2 + 3x + 7$

    $\displaystyle y = -2x + x + 9$

    Can you do this?
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Step 1: Solve the following equations simultaneously:

    $\displaystyle y = x^2 + 3x + 7$

    $\displaystyle y = -2x + x + 9$

    Can you do this?
    sorry, the 2 equation are:

    $\displaystyle y = x^2 + 3x + 7$

    $\displaystyle y = -2x^2 + x + 10$

    to get points of intersection:

    $\displaystyle x^2 + 3x + 7$ = $\displaystyle -2x^2 + x + 10$
    $\displaystyle 3x^2 + 2x - 3 = 0$

    solving for x = $\displaystyle \frac{-1 \pm \sqrt{10}}{3}$

    we find y for each x, and use the 2 points with the third (2 , 1) to solve for A, B, and C in:

    $\displaystyle f(x) = Ax^2 + Bx +C$

    but the question says use a simple way to find the function !!!
    is this a simple way ??
    Last edited by razemsoft21; Apr 29th 2009 at 06:51 AM.
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