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Homework Help: Find Equation for the Parabola- Help, Please?

  1. May 12, 2004 #1
    Each pair of the following three lines cross at a point. Those points are the y-intercept, one of the x-intercepts, and the vertex of a parabola. Can you please explain to me how to find an equation for the parabola? And the other x- intercept?

    y+8x=32
    y+5x=32
    y+3x=12

    I have been trying everything I can think of. I think they cross at 0. And I know the equation has to be squared, but I'm so lost on this one, I don't know what else to do. Any advice would be appriciated. Thank you.
     
  2. jcsd
  3. May 13, 2004 #2

    arildno

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    Step 1:
    Determine the 3 pairs of (x,y)-values that solves the 3 pairwise systems of linear equations.
    Let's call these:
    [tex] {r}_{1}=(x_{1},y_{1}),
    {r}_{2}=(x_{2},y_{2}),
    {r}_{3}=(x_{3},y_{3})
    [/tex]

    Step 2.
    The general equation for a parabola when the y-coordinate is a function of the x-coordinate is:
    [tex]
    y=ax^{2}+bx+c[/tex], where a, b,c are constants.

    You do know something of the parabola you're after, namely that the 3 pairs [tex] r_{1},r_{2},r_{3}[/tex] are on it.
    How can this information be used in order to determine a,b,c?
     
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