I have a problem with the Intermediate value theorem. For example if I have the function $(x)=-4x^2+12x$, I can get for example all the values from $x=0$ to $x=2$, so $f(0)=0$ and $f(2)=8$, with the Intermediate value theorem, I know that the function takes all the values from $0$ to $8$. But it also takes the value $9$ when $x$ goes from $0$ to $2$, so with the Intermediate value theorem I can´t know all the value that the function takes.

Can anyone explain me why this happens in this example, and obviously in other example.