\(A=-2x^2+2\left|x\right|-5=-\dfrac{1}{2}\left(4x^2-4\left|x\right|+1\right)-\dfrac{9}{2}=-\dfrac{1}{2}\left(2\left|x\right|-1\right)^2-\dfrac{9}{2}\le-\dfrac{9}{2}\)
\(A_{max}=-\dfrac{9}{2}\) khi \(\left|x\right|=\dfrac{1}{2}\Rightarrow x=\pm\dfrac{1}{2}\)