a) $A = x^2 + x$
$\to A = \left(x + \dfrac{1}{2}\right)^2 - \dfrac{1}{4}$
$\to\min A = -\dfrac{1}{4}\Leftrightarrow x = -\dfrac{1}{2}$
b) $B = ax^2 + bx + c$
$\to B = a\left(x^2 + 2.\dfrac{b}{2a}x+ \dfrac{b^2}{4a^2}\right) + c -\dfrac{b^2}{4a}$
$\to B = a\left(x + \dfrac{b}{2a}\right)^2 + c -\dfrac{b^2}{4a}$
Với $a > 0$
$\to \min A = c -\dfrac{b^2}{4a}\Leftrightarrow x = -\dfrac{b}{2a}$
Với $a < 0$
$\to \max A = c -\dfrac{b^2}{4a}\Leftrightarrow x = -\dfrac{b}{2a}$
c) $C = 8x^2 + 12x + 50$
$\to C = 8\left(x +\dfrac{3}{4}\right)^2 +\dfrac{91}{2}$
$\to \min C = \dfrac{91}{2}\Leftrightarrow x = -\dfrac{3}{4}$
