Ta có: \(P=-x^2+2x+5\)
\(=-x^2+2x-1+6\)
\(=-\left(x-1\right)^2-6\)
Vì \(-\left(x-1\right)^2\le0;\forall x\)
\(\Rightarrow-\left(x-1\right)^2-6\le0-6;\forall x\)
Hay\(P\le-6;\forall x\)
Dấu "="xảy ra \(\Leftrightarrow\left(x-1\right)^2=0\)
\(\Leftrightarrow x=1\)
Vậy MAX P=-6 khi x=1