Question 36
Let $n \geq 1$ be a positive integer. For every $k = 1, 2, \ldots, n$ the functions $f_k: \mathbb{R} \rightarrow \mathbb{R}$, $f_k(x) = a_k x^2 + b_k x + c_k$ with $a_k \neq 0$ are given. Find the greatest possible number of parts of the rectangular plane $xOy$ which can be obtained by the intersection of the graphs of the functions $f_k$ ($k = 1, 2, \ldots, n$).