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Math Help - Finding Equation of a Parabola?

  1. #1
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    Finding Equation of a Parabola?

    Determine the equation of the parabola:

    Given two points at (-4,9) and (12,9). I figured out the axis of symmetry is x=4. Also given the y-intercept, which is (0,-3). Figure out the equation?

    Thanks for the help!
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  2. #2
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    Re: Finding Equation of a Parabola?

    Write the parabola in the form y = a(x-b)^2 + c where a,b,c are constants and a \neq 0.


    It is symmetric about x = 4, so letting b = 4 yields our desired parabola.


    Now our parabola is in the form y = a(x-4)^2 - c. Subsitutute the given values of (x,y) to obtain a system of equations in terms of a and c.
    Last edited by richard1234; July 30th 2012 at 08:35 AM.
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  3. #3
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    Re: Finding Equation of a Parabola?

    Quote Originally Posted by woahitzme View Post
    Determine the equation of the parabola:
    Given two points at (-4,9) and (12,9). I figured out the axis of symmetry is x=4. Also given the y-intercept, which is (0,-3). Figure out the equation?
    Get a sheet of graph paper and plot those 2 points. Then come back and post your question correctly.
    If you can't tell right away that y-intercept is (0,9), then you need classroom help.
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    Re: Finding Equation of a Parabola?

    Quote Originally Posted by Wilmer View Post
    Get a sheet of graph paper and plot those 2 points. Then come back and post your question correctly.
    If you can't tell right away that y-intercept is (0,9), then you need classroom help.
    It's a parabola, not a line.
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  5. #5
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    Re: Finding Equation of a Parabola?

    Quote Originally Posted by woahitzme View Post
    Determine the equation of the parabola:

    Given two points at (-4,9) and (12,9). I figured out the axis of symmetry is x=4. Also given the y-intercept, which is (0,-3). Figure out the equation?

    Thanks for the help!
    The quadratic has the equation \displaystyle \begin{align*} y = a\,x^2 + b\,x + c \end{align*}. Substituting the y-intercept \displaystyle \begin{align*} (0, -3) \end{align*} yields \displaystyle \begin{align*} c = -3 \end{align*}, giving \displaystyle \begin{align*} y = a\,x^2 + b\,x - 3 \end{align*}.

    Substitute each of the other points and solve the two equations simultaneously for a and b.
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    Re: Finding Equation of a Parabola?

    Quote Originally Posted by richard1234 View Post
    It's a parabola, not a line.
    Yikes...guess I'm the one who needs classroom help !!
    Thanks from a tutor
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    Re: Finding Equation of a Parabola?

    Quote Originally Posted by richard1234 View Post
    Write the parabola in the form y = a(x-b)^2 + c where a,b,c are constants and a \neq 0.


    It is symmetric about x = 4, so letting b = 4 yields our desired parabola.


    Now our parabola is in the form y = a(x-4)^2 - c. Subsitutute the given values of (x,y) to obtain a system of equations in terms of a and c.
    I plugged in (-4,9) as well as the y-intercept which was -3 for c. I got  9= a(8)^2 - 3 and ended up getting  a= 3/16 .

    The book answer is that the equation is  1/4 x^2 - 2x -3 .
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    Re: Finding Equation of a Parabola?

    Nevermind, I got the answer, thank you guys!
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