Find the equation to the curve that joins the following points.

Question

(1,1),(0,1),(2,5),(-1,-5)

Answer 1

assuming you want a polynomial of lowest degree, that would be a cubic

y=ax^3+bx^2+cx+d
(1,1): a+b+c+d=1
(0,1): d=1
(2,5): 8a+4b+2c+d=5
(-1,-5): -a+b-c+d=-5

solve the system to get (and avoiding fractions)

3y = 5x^3-9x^2+4x+3