bài 10:
\(•A\left(x\right)=4x^2-4x+3=4x^2-4x+1+2\\ A\left(x\right)=\left(2x-1\right)^2+2\\ vì\: \left(2x-1\right)^2\ge0\: \forall x\in R\: do\: đó\: A\left(x\right)>0\: \forall x\in R\: \)
\(•B\left(x\right)=2x-x^2-7=-\left(x^2-2x+1+6\right)\\ B\left(x\right)=-\left(x-1\right)^2-6\\ vì\:-\left(x-1\right)^2\le0\: \forall x\in R\: \:do\:đó\:B\left(x\right)< 0\: \forall x\in R\: \)
\(•C\left(x\right)=ax^2+bx+c\\ C\left(x\right)=a\left(x^2+\dfrac{b}{a}x\right)+c\\ C\left(x\right)=a\left(x^2+2.\dfrac{b}{2a}+\dfrac{b^2}{4a^2}-\dfrac{b^2}{4a^2}\right)+c\\ C\left(x\right)=a\left(x+\dfrac{b}{2a}\right)^2-\dfrac{b^2}{4a}+\dfrac{4ac}{4a}\\ C\left(x\right)=a\left(x+\dfrac{b}{2a}\right)^2+\dfrac{4ac-b^2}{4a}\)