How can I determine if my telescope mirror is parabolic? This week I purchased the “Skywatcher Explorer 130P Newtonian Reflector Telescope”,  specifically as it has the parabolic mirror. I do not have the outer packaging for sundry reasons. Therefore, after setting up the telescope, how can I check to see whether my telescope is actually a version with the parabolic mirror or the standard mirror. 
The manuals that came with it do not tell you this, nor I am versed in spotting one from the other just by looking at it.
Are there any tests I can do, or is there a ‘quick check’ to ascertain the parabolic mirror is on the telescope?
 A: It's a pretty complex topic. Bottom line: if the scope is doing okay, it's probably parabolic.
The one way to tell for sure, and even ascertain figuring errors and whatnot, is to do a proper optical test. If I was in that situation, I would just take the mirror out, put it on the Foucault / Ronchi tester, and take some measurements. A ronchigram would give a qualitative answer immediately: is it a parabola-like curve or not? Are there any gross errors or not? Then a quantitative Foucault test could actually provide some numbers.
You could google the Foucault test and the Ronchi test for telescope mirrors if you're curious.
With the mirror installed in the scope, it's a bit more complex. One thing is certain: at an f/5 focal ratio, if it's not parabolic, performance would be pretty terrible. Even if it is parabolic, this being cheap mass-produced optics, some issues may remain. Even assuming a very expensive, near-perfect parabola, at f/5 an aberration called coma will be pretty obvious (it's a defect of this geometry, still exists even with perfect optics).
One thing you could do is learn star testing. It's not trivial, but it could reveal various issues. Google this topic, it's pretty big. Some links to get you started:
http://legault.perso.sfr.fr/collim.html
http://www.astrosurf.com/altaz/startest_e.htm
One outcome of star testing is that you'll get your scope collimated really really well, which is something you should do anyway. Once that's done, start looking for spherical aberration. A good parabola will show only a residual amount of spherical aberration; a top-shelf perfect parabola will show zero spherical aberration. At f/5, a pure sphere will show horrible amounts of this aberration.
At first, you'll be liable to confuse spherical aberration with turned down edge (assuming your scope exhibits both). Also, the central obstruction (the edge of the secondary mirror) will distort the diffraction figure in ways that could be mistaken for aberration, if you're not very familiar with it. Keep experimenting and learning and you'll figure it out eventually.
Use a good quality, strong eyepiece for the star test. Keep the image in the exact center, to reduce extra issues with the eyepiece. Polaris is a good star for testing, since it doesn't move and it's bright enough. Don't do the test when seeing is bad and the diffraction figure is shaking like a bowl of jello.
A: Doing a star test, as Florin suggests, is the correct and general reply to telling the difference between a parabolic and a spherical mirror. But in this specific situation of telling between a SkyWatcher 130mm reflector, there's a much simpler way. The two SkyWatcher 130mm reflectors have a second major difference between the spherical and parabolic versions: the two telescopes have very different focal lengths. The parabolic version has a focal length of 650mm (f/5) while the spherical version has a  much longer focal length, 900mm (f/6.9). As a result, the tube on the spherical version is about 50% longer, about 35 inches, as opposed to about 25 inches on the parabolic version.
