[tex] f(x)=ax^2+bx+c[/tex]
=[tex] a(x^2+\frac{bx}{a})+c [/tex]
=[tex]a(x^2+2. \frac{bx}{2a}+\frac {b}{2a}^2 - \frac{b^2}{4a^2} ) [/tex]
=[tex]a(x+\frac{b}{2a})^2 +( \frac{-b^2}{4a} +c) [/tex] >= m
+) Neu a>o => f(0) >= m voi moi x
=> f(x) >=m voi moi x
=> f(x) co GTNN=m
<=> [tex] x= \frac{-b}{2a} [/tex]
+) Neu a<0 => f(x) <= m voi moi x
=> f(x) co GTLN =m <=> [tex] x= \frac{-b}{7a}[/tex]