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Parabola equations review

  1. Aug 26, 2007 #1
    1. The problem statement, all variables and given/known data
    Write the equation for the parabola. Vertex (0,0), axis along x-axis, passes thru (-2,-4).

    3. The attempt at a solution

    I thought since the parabola resides on the x-axis that I was supposed to use x^2=4py, with a parabola looking similar to this:


    However, the solution is actually in the form of y^2=4py, looking like this:


    I thought if it was along the x-axis it would look similar to the first pic? (This problem is just a refresher for the technical calc course I'm enrolled in, sorry for the crappy mspaint pics)
  2. jcsd
  3. Aug 26, 2007 #2
    It seems that you have confused the plots of the parabolas with respect to their equations.
    Assuming you have your axes right (x+ point to the right, y+ point up) parabolas of the form "x^2 = 4py" correspond to the 2nd image you attached, while those of the form "y^2 = 4px" correspond to the 1st one.

    This is easy to see, as -in the "x^2 = 4py" case- for each y you should have too solutions for x (since x is squared), therefore the symmetry must be with respect to Y, thus the 2nd image.
  4. Aug 26, 2007 #3
    I think I'm confused because the problem says axis along x-axis; in this case, I thought 'along the x axis' meant the equation x^2=4py would be used. The book, however, says y^2=4py is to be used...
  5. Aug 26, 2007 #4
    anybody? This seems to be a very simple but I can't figure out why I cannot visualize this problem.
  6. Aug 26, 2007 #5


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    "axis" means "axis of the parabola". I believe the wording would have been clearer if your book said, "axis of the parabola... parallel to the x axis". "Along", as used was intended to mean "in the same direction as..."; my opinion is that it is a little more difficult to interpret.
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