Zeroes at 1±sqrt(2) ,y-intercept at –4

Question

f(x)=?

Answer 1

many functions meet those criteria, but one of them is

given roots:
y = (x - (1+√2))(x-(1-√2))
= x^2-2x-1

That has a y-intercept of -1. So, multiply it by 4. It has the same roots, but now y(0) = -4.