Mcl116--LiveJazz is right--there's a lot going well in your turns, especially if you haven't had much time to develop your skills. You use your edges effectively, especially at the end of your turns, to grip and hold the line you're trying to ski. You turn your skis primarily with your legs, as opposed to heaving them around with gross movements of your upper body (a movement pattern that haunts the vast majority of recreational skiers). It looks to me like you have the skill to get your skis to do pretty much whatever you want them to do, most of the time.
So the question is--what do you want them to do? Most of your turns begin abruptly, with fairly intense movements to twist your skis and get onto the new edges. Then those movements become minimal, once you get the turn started. The result is a very "Z"-shaped line, with little roundness to your turn finishes. With your skill set, there's no reason your turns have to be this shape, so I must assume that somewhere, perhaps unconsciously, you want your turns to be this shape.
My suggestion is to focus on your tactics first, before trying to make any of the technical changes others have suggested. Visualize your turns being rounder, with more "patient" starts, more time spent in the middle with your skis and body traveling down the hill, and more activity at the end to maintain the round shape and finish the turn--perhaps even traveling a little uphill before starting the next turn. Rounding the turns will involve decreasing the intensity while increasing the duration of your movements and efforts. This tactical focus will hold in all of your turns, large and small, and in all conditions, including the short, quick turns of bumps.
Changing your tactics will, all by itself, begin to change some of your movements. When you aren't in such a rush to get through the turn, you are less likely to use your upper body and more likely to begin your movements lower down, as Josh has suggested.
From your movements, I assume that you've had at least a little instruction sometime in the past. If you really want to improve in your few days on skis, I cannot highly enough recommend that you seek out a good instructor and get some guidance and focus in real time, on the snow. But go out and play with a rounder and more complete turn shape first and see how it goes. Then jump in on a lesson to get the wrinkles ironed out.