Question

Hi ! How to solve this question?

Answer 1

You should actually have

$-x^2-4x-10=-(x^2+4x+10)=-(x^2+4x+4+6)=-((x+2)^2+6)=-(x+2)^2-6$

Now, remember that $x^2$ is always non-negative, so $(x+2)^2\ge0$ for any value of $x$. This means $-(x+2)^2\le0$ for any $x$, and so

$-(x+2)^2-6\le0-6=-6$

i.e. f(x) is at most -6, and hence negative for all $x$.