Why Use y^2=4px for a Parabola with Axis Along x-Axis?

[fitz_calc]

Homework Statement

Write the equation for the parabola. Vertex (0,0), axis along x-axis, passes thru (-2,-4).

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)

 

[sidman]

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.

 

[fitz_calc]

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...

 

[fitz_calc]

anybody? This seems to be a very simple but I can't figure out why I cannot visualize this problem.

 

[symbolipoint]

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...

"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.