I want to show that $\displaystyle ax^{2}+bx+c$ is nither injective nor surjective where $a,b,c\in \mathbb{R}$ and $a\neq 0$. Can i use the following result?
If $f$ is a continuous real valued function on interval $I$ and if $f'(x)>0$ for all $x$ in $I$ except possibly at the end points of $I$, then $f$ is one-to-one.
Here $f(x)=ax^{2}+bx+c$ being a polynomial so it is continuous in $R$ but $f^{'}(x)=2ax+b$ attains both signs that's why $f$ is not injective. And for surjective: for $y=ax^{2}+bx+c $, there does not exist any $x\in R$ such that $f(x)=y.$ Am i right?