Find the equation of the image of the curve y = x² after each of the following combinations of transformations and, in each case, sketch the graph of the resulting curve.
a. A stretch in the x-direction with factor 2 followed by a translation by the vector 

b. A translation by the vector 

followed by a stretch in the x-direction with factor 2

c. On a graph show the curve y = x² and each of your answers to parts a and b.

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