Irish Math Olympiad 2018 Paper 1 - Problem 3 скачать в хорошем качестве

Irish Math Olympiad 2018 Paper 1 - Problem 3

Latex: Find all functions $f(x) = ax^2 + bx + c$, with $a
e 0$, such that $f(f(1)) = f(f(0)) = f(f(-1))$. Timestamps: 00:00 Intro 15 - 30/45 - 90 Take 15 00:23 Trying to understand the problem 00:38 Approach 1 to the problem 01:02 Approach 2 to the problem 01:30 Trying a general idea in functions 03:30 What does a quadratic function look like 04:20 The idea 05:25 The logic of the idea 06:10 The next part of the idea 07:40 Getting back to the problem 08:45 Case 1) b = -a 09:45 Applying the same core idea AGAIN! 11:10 Finding the first function and checking it 11:55 Completely unnecessary and wrong part 12:51 Fixed the mistake and finished checking 15:20 Case 2) a = b 17:24 Checking the algebra 18:00 Case 3) b = 0 19:10 Checking the algebra again 19:50 Reflecting on the problem 25:25 Thanks for problem solving :)