Let consider the function $$f(t)=a t^2+b$$, and the line $D$ defined by $$y=mx+p$$ such that the constants $(a,b,m,p$) are real and $(a\neq 0,b\neq 0,m\neq 0,p\neq 0)$
What is the expression of the function $g$ such that $g$ and $f$ are symmetric with respect to $D$ ?