9.6. Petya and Vasya came up with ten quadratic trinomials. Then Vasya sequentially named consecutive natural numbers (starting from some number), and Petya substituted each named number into one of the trinomials of his choice and wrote down the obtained values on the board from left to right. It turned out that the numbers written on the board form an arithmetic progression (in this exact order). What is the maximum number of numbers Vasya could have named?

(A. Golev)