If John charge $12 then he has 14 students, and he gets $ 14*12,
If he increases on $2(12+2) , he loses 1 student (14-1), gets (12+2)*(14-1)
if he increases on he loses 2 students (14-2) gets (12+2*2)(14-2)
2+2 (12+2*2)
if he increases 2*3 he loses 3 students, (14-3) gets (12+2*3)(14-3)
2x*3 (12+2*3)
and so on......
if he increases 2*x, he loses x students, (14-x)left, gets (12+2x)(14-x)
(12+2x)
So , his revenue in general =
(12+2x)(14-x)=12*14-12x+28x-2x²=-2x²+16x+168
I think it should look like this
c(x)= -2x²+16x+168