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Quadratic function is pinned down

Source: 2022 Bulgarian Spring Math Competition, Problem 9.1

March 27, 2022
algebraquadratic trinomialquadraticsfunction

Problem Statement

Let f(x)f(x) be a quadratic function with integer coefficients. If we know that f(0)f(0), f(3)f(3) and f(4)f(4) are all different and elements of the set {2,20,202,2022}\{2, 20, 202, 2022\}, determine all possible values of f(1)f(1).
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