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Parabola question

  1. May 14, 2008 #1
    mods please move this topic if this is not in the correct section. thanks. :)

    the question is:
    the vertices of the family of parabolas y = x^2 + bx, b is constant, lie on a single parabola. Find equation for that parabola.

    my teacher require me to provide supporting details & background info that back up my answer and have to verify it using a different method. i'm really puzzled and i would greatly appreciate any help that comes my way. thanks in advance.
     
  2. jcsd
  3. May 15, 2008 #2
    Well why don't you start by showing what you've done on the problem, and we'll take it from there.
     
  4. May 15, 2008 #3

    HallsofIvy

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    You might want to start by completing the square so it's easy to see where the vertices are.
     
  5. May 15, 2008 #4
    so this is what i've gotten so far, please correct me if i'm wrong.

    for any generalized parabola, the equation is given in the standard form: y = ax^2 + bx + c

    a = 1 (in the equation y = x^2 + bx)
    b = constant
    c = (b/2)^2

    the equation for the parabola that the question asks for, if written as completing the square, should be: y - k = (x - h)^2.
    we need to find the center (h, k) so that y = x^2 + bx.

    y - k = (x - h)(x - h)
    y - k = x^2 - 2xh + h^2

    ...?
     
  6. May 15, 2008 #5
    [tex]x^2+bx=(x+b/2)^2-b^2/4[/tex] check it and then see if that's helpful for you.
     
  7. May 17, 2008 #6

    HallsofIvy

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    Yes, but not in this equation! Would it be easier to write it as [itex]y= a(x^2+ (b/a)x)+ c[/itex]? How would you complete the square for [itex]a(x^2+ (b/a)x[/itex]?

    Why, after completing the square, did you then ignore it?
     
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