How to choose parametric regression model with two predictors

I have a response variable (depicted on the y-axis in the following plots), that I want to regress using two predictors.

On each plot, one predictor is along the x-axis, the other is color-coded in the points.

If I were using a single predictor, I would model the relationship between the first predictor and the response variable as an exponential:

$$ y = a e^{-bx} + c $$

And the relationship with the second, using a quadratic relationship:

$$y = ax^2 + bx + c$$

How would you model both predictor relationships at the same time (considering also the interaction between them)?