Question 906001
Infinitely many polynomials can contain those four points.  Pick as low a degree function as you can.


A root occurs between x at -2 and -1.
A root occurs between x at -1 and 2.
We do not expect a root between x at 2 and 3.


The function f may be degree 3 with a positive leading coefficient.  From -1 to 2, f decreases, and from 2 to 3, f increases.


{{{ax^3+bx^2+cx+d=y}}} can be the general form for the cubic equation, and specific equations can be made from each of the four given points.  Setup a system of equations and solve for a, b, c, and d.


{{{system(a(-2)^3+b(-2)^2+c(-2)+d=-1,a(-1)^3+b(-1)^2+c(-1)+d=7,a^2^3+b*2^2+c*2+d=-5,a*3^3+b3^2+c*3+d=-1)}}}


Simplify the equations; Solve the system any way you know.


(Yes, those are FOUR different equations, but they are a SYSTEM OF EQUATION.  They are linear in the variables, a, b, c, d.  They are based on the a general form from the cubic equation which is still unknown, {{{ax^3+bx^2+cx+d=y}}}).