Generate a random nonlinear function going through given points in python
It looks more like a math problem to me here, since you ask "how to start".
you know that a function's plot is just a lot of points (x, y) where y=f(x).
And I know that for any two pairs of points (not vertically aligned), I have an infinity of second-degree functions (parabolas) going through these two points.
they are given by y=ax^2+bx+c 
You want the parabola to go through your 2 points, so you can substitute x and y for each of the 2 points, that will give you 2 equations (where a, b and c are the unknown) .
Then you can add a random point (I would suggest on the y-axis :  (0; r) ).
This will give you a third equation.
With these 3 equations, solve for a, b and c. (in function of r)
now, for any value of r, you will have some a, b and c that define a parabola going through your 2 known points.
Once you understand how to solve this math problem, the python part is completely independant.
I have two given points (3.0, 3.2) and (7.0, 4.59) .
My job here is very simple but I don't even know how to start. I just need to plot 4 nonlinear functions that go through these two points.
Did somebody have a similar problem before? How does one even start?