# Is it possible to train an RNN to predict projectile motion?

Projectile motion is given by a function $$y = -9.81 x^2 + ax + b$$ for some parameters $$a$$ and $$b$$. I'll simply assume for $$x$$ values to be distanced by 1, so $$x_t = t$$. I can then easily generate series $$y_0, \dots, y_n$$ of arbitrary lengths and parameters $$a, b$$. For simplicity, we can assume that the values stay within some bound, e.g. from -1000 to 1000, so that activation functions can still be used.

Is it (theoretically) possible to train an RNN such that for an input series $$y_0, \dots, y_n$$ it will correctly output the value $$y_{n+1}$$? Or is the quadratic part in the definition of $$y$$ not something that an RNN can ever compute?

Note that I'm not talking about some approximation on a compact domain but actual precise computation of the target value.