Question: How to plot a 3D curve using implicit equations for each coordinate?

For example, 

f(x,t) = t^2 x^2 + t x + 2x - 1g(y,t) = t^2 y^3 + t y^2 + 2y - 1h(z,t) = 2t^2 z^3 + t z + 3z - t^2, 0 < t < 4.

I have an initial point on the curve corresponding to t=0.  The answer is a curve in space, or maybe several curves.  The real example that I care about is much more complex than this and has trig functions of t.

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