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Problem 575

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

50. (VIE 4) Find a function $f(x)$ defined for all real values of $x$ such that for all $x$ ,
$f(x+2)-f(x)=x^{2}+2 x+4,$
and if $x \in[0,2)$ , then $f(x)=x^{2}$ .

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

None

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.