I have a set of points that define a function like this $[(0,6),(1,2),(3,8)]$. I want to find a function $f(x)$ which satisfies these conditions.
Note : I know many people will say there are infinite possibilities, I know that. I just want to find a function with these points I don't care for the other points.
On
Since the required function satisfied given three points $(0,6),(1,2) \text{and} (3,8)$, so from there you can conclude that if you want to use a polynomial function then $2^{\text{nd}}$ degree polynomial function is the smallest degree polynomial. So let it be of the form $$f(x)=ax^2+bx+c$$where the constants $a,b, c$ are found by satisfying the points on the function.
Therefore you can follow the rule described by @Cornman.
Write $y = ax^2 + bx + c$. Now substitute in your three points. You will have three equations in three unknowns (linear). Solve for $a$, $b$, and $c$.