\(1,\\ B=\left(x^2-8x+16\right)-14=\left(x-4\right)^2-14\ge-14\\ B_{min}=-14\Leftrightarrow x=4\\ Q=\left(x^2+2x+1\right)+2=\left(x+1\right)^2+2\ge2\\ Q_{min}=2\Leftrightarrow x=-1\\ A=\left(x^2+4x+4\right)+1=\left(x+2\right)^2+1\ge1\\ A_{min}=1\Leftrightarrow x=-2\\ P=\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\\ P_{min}=\dfrac{3}{4}\Leftrightarrow x=\dfrac{1}{2}\\ 2,\\ P=2\left(x^2-6x+9\right)-18=2\left(x-3\right)^2-18\ge-18\\ P_{min}=-18\Leftrightarrow x=3\)
\(Q=5\left(x^2+2x+1\right)-5=5\left(x+1\right)^2-5\ge-5\\ Q_{min}=-5\Leftrightarrow x=-1\\ A=3\left(x^2+4x+4\right)-18=3\left(x+2\right)^2-18\ge-18\\ A_{min}=-18\Leftrightarrow x=-2\\ B=2\left(x^2-4x+4\right)+4=2\left(x-2\right)^2+4\ge4\\ B_{min}=4\Leftrightarrow x=2\\ 3,\\ P=-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{1}{4}=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\\ P_{max}=\dfrac{1}{4}\Leftrightarrow x=\dfrac{1}{2}\\ Q=-\left(x^2+4x+4\right)+11=-\left(x+2\right)^2+11\le11\\ Q_{max}=11\Leftrightarrow x=-2\\ A=-\left(x^2-x+\dfrac{1}{4}\right)-\dfrac{37}{4}=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{37}{4}\le-\dfrac{37}{4}\\ A_{max}=-\dfrac{37}{4}\Leftrightarrow x=\dfrac{1}{2}\)
\(B=-\left(x^2+8x+16\right)+25=-\left(x+4\right)^2+25\le25\\ B_{min}=25\Leftrightarrow x=-4\\ 4,\\ P=-2\left(x^2-6x+9\right)+18=-2\left(x-3\right)^2+18\le18\\ P_{max}=18\Leftrightarrow x=3\\ Q=-5\left(x^2-2x+1\right)+5=-5\left(x-1\right)^2+5\le5\\ Q_{max}=5\Leftrightarrow x=1\\ A=-3\left(x^2-4x+4\right)+11=-3\left(x-2\right)^2+11\le11\\ A_{max}=11\Leftrightarrow x=2\\ B=-2\left(x^2-12x+36\right)+84=-2\left(x-6\right)^2+84\le84\\ B_{max}=84\Leftrightarrow x=6\)
