a,
$f(x)= x^2-4x+2= x^2-4x+4-2 = (x-2)^2-2$
$(x-2)^2\ge 0 \Rightarrow f(x)\ge -2$
$\text{min f(x)}= -2 \Leftrightarrow x=2$
b,
$g(x)= -x^2+x+1= -x^2+2x.\frac{1}{2}-\frac{1}{4}+\frac{5}{4}= -(x-\frac{1}{4})^2+\frac{5}{4}$
$-(x-\frac{1}{2})^2\le 0 \Rightarrow g(x)\le \frac{5}{4}$
$\text{max g(x)}=\frac{5}{4}\Leftrightarrow x=\frac{1}{2}$