



 
Hi Stephanie, You gave the answer as x = 2  t, y = 2(2  t)  (2  t)^{2} but you missed an important part of the answer. You didn't give the domain of t and without it you don't know which part of the parabola you are parameterizing. You need to say
Now you can see that when t = 0, x = 2 and y = 0 and when t = 2, x = 0 and y = 0. Thus the parameterization is for the piece of the parabola from (2,0) to (0,0) but not only that, as t increases you are moving from (2,0) to (0,0). There are many ways to parameterize a curve and this is not the only answer to your problem. When I first read your problem I thought of the parameterization x = s and y = 2s  s^{2}. In this case the point (2,0) comes from s = 2 and the point (0,0) comes from s = 0. Thus I get
With this parameterization as the parameter s increases you move along the curve from (0,0) to (2,0). I hope this helps,  


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