--> f : a · x ^ 2 + b · x + c ;

\[\operatorname{ }a {{x}^{2}}+b x+c\]

--> diff ( f , x , 1 ) ;

\[\operatorname{ }2 a x+b\]

--> integrate ( f , x ) ;

\[\operatorname{ }\frac{a {{x}^{3}}}{3}+\frac{b {{x}^{2}}}{2}+c x\]

--> sol : solve ( [ f = 0 ] , [ x ] ) ;

\[\operatorname{ }\left[ x=-\frac{\sqrt{{{b}^{2}}-4 a c}+b}{2 a}\operatorname{,}x=\frac{\sqrt{{{b}^{2}}-4 a c}-b}{2 a}\right] \]

--> sol ;

\[\operatorname{ }\left[ x=-\frac{\sqrt{{{b}^{2}}-4 a c}+b}{2 a}\operatorname{,}x=\frac{\sqrt{{{b}^{2}}-4 a c}-b}{2 a}\right] \]

--> g : subst ( [ a = 3 , b = 4 , c = 2 ] , f ) ;

\[\operatorname{ }3 {{x}^{2}}+4 x+2\]

-->
--> wxplot2d ( [ g ] , [ x , − 5 , 5 ] ) $

\[\operatorname{ }\]

(Graphics)

Created with wxMaxima.

The source of this Maxima session can be downloaded here.