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`.