how do you change a Cartesian equation to a parametric function?
Cartesian as in y = e^(2x-1) and parametric as in x = [something] and y = [something]. how do you convert?
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The easiest way is let x = t and y = f(t)
So for your example, x = t, y = e^(2t-1)
some suggestions... in case you finished the sq., you get (x-2)=(y-3)^2 which shows its a parabola (not a hyperbola) dealing with appropriate with its vertex at (2,3) as you propose. In parametric style you ought to write y = t +3 and x = t^2 + 2 the place t is the parameter.