I don't know how much you know or don't know, so apologies if this seems simplistic.
Highlighting the shape with the Magic Wand tool. This will create a marquee (like a line of marching ants.)
In the Paths window (open it from the Windows menu), click on the small Path icon in the bottom row (like a circle with a tangential line either side.) This will create a path from the marquee.
You now have your path. Click on the Pen tool in the toolbar to amend it.
If you have trouble creating a marquee, try duplicating the parabolic line (highlight the line, copy and paste it and then Flip either Horizontal or Vertical in Transform points in the Edit menu) to create a shape, follow the guide above and then later delete half of the shape to revert to your original line.
You can change the path's shape using the handles (which change the angle of the line either side of the relevant anchor point). Hold down the Ctrl or the Command key while grasping the handle - the icon will change to a white arrow, indicating manoeuvrability.
If you hold down the alt key while clicking a handle, the handle will be deleted, fixing the angle of the line on that side.
You can add anchor points by clicking on the line whilst in Pen mode. Remove anchor points by clicking on them in Pen mode.
Look carefully at the Pen icon while you're using it - you will see either a + (meaning add) or a - (meaning delete).
There are surely websites out there that will give you better tuition on manipulating paths, but this is a rudimentary guide.
And, as in all things, the key to success is practice, practice, practice.
Hope this helps - good luck.