Implementing a polynomial voltage-controlled current source in LTSpice
The POLY source is old as SPICE itself (40+ years). The better choice is to use a behavioural source (voltage or current), not only because it makes things easier in terms of implementing a mathematical expression, but also because LTspice will replace it, behind the scene, with a behavioural source, anyway. This is how the expression would look like:
V = a0 + a1*V(x) + a2*V(x)**2
where I presumed to be V(x) instead of V. It's not necessary to use voltages, currents and other time-dependent quantities are allowed, with some conditions. Read more in the help, under LTspice &gt; Circuit Elements &gt; B. Arbitrary Behavioral Voltage or Current Sources.
Note the exponentiation, **, not ^ (which means XOR, unless it's a Laplace expression). If you're using a current source, then it would be I = ....