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Finding a parabola given two x intercepts

  1. Sep 24, 2008 #1
    If you are given (5,0) and (-1,0) as the two x intercepts of a parabola is it possible to find the equation of the parabola? I have tried using the vertex formula for the x co-ordinate which is x = 2 the line of symmetry and plugging in either of these co-ordinates into y = ax^2 + bx + c but have too many unknowns to solve for. Is this unsolvable with only this information?
     
  2. jcsd
  3. Sep 25, 2008 #2

    symbolipoint

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    This is possible only if you are looking for a general parabola; NOT for a specific one. In fact, you need THREE points to establish a specific parabola.
     
  4. Sep 25, 2008 #3

    Mentallic

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    Only being given the roots of the parabola isn't sufficient enough to compile a specific parabola from it. There are an infinite number of parabolas having those 2 roots, all having different "steepness" and concavity.

    e.g.

    [tex]y=(x-5)(x+1)[/tex]
    [tex]y=2(5-x)(3x+3)[/tex]

    etc.
     
  5. Sep 25, 2008 #4
    Thanks. I suppose if I tried different values for a and b I would come up with different parabolas. Wasn't sure if there was some way with the line of symmetry to determine the y value of the vertex but I realize that there are different options with only two points. Thanks again.
     
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