input courbes.mp;
verbatimtex 
%&latex 
\documentclass{article} 
\usepackage{palatino} 
\newcommand{\vect}[1]{\overrightarrow{#1}}
\newcommand{\Vect}[1]{\overrightarrow{\strut #1}}
\begin{document} 
etex 

beginfig(1);
numeric u;
u = 1cm;
z0=(0,0);z1=(7u,0u);z2=(2u,0);z3=(5u,0);z4=(2u,0.5u);z5=(5u,0.5u);
z6=(0.5u,0);z7=(6.5u,0);z8=(2u,1.5u);z9=(2.5u,1.5u);z10=(5u,1.5u);z11=(2.5u,-1.5u);
z12=(3.5u,-u);z13=(3.5u,-0.5u);z14=(2u,-0.5u);z15=(5u,-0.5u);

%creation de l'axe et des flèches
draw z0--z1;
drawarrow z8{left}..z6{down}; drawarrow z10{right}..z7{down};
draw z2+(0,-0.1u)--z2+(0,0.1u); draw z3+(0,-0.1u)--z3+(0,0.1u);
drawarrow z12--z13;
pickup pensquare scaled 2pt;
draw z0--z2; draw z3--z1;
pickup pencircle scaled 1pt;

%le texte
label.bot(btex $0$ etex, z4); label.bot(btex $0$ etex, z5);
label.rt(btex signe de $a$ etex,z9); label.rt(btex signe de -$a$ etex,z11);
label.top(btex $x_1$ etex, z14); label.top(btex $x_1$ etex, z15);

endfig;

beginfig(2);
numeric u;
u = 1cm;
z0=(0u,0u);z1=(7u,0u);z2=(3.5u,0u);z3=(3.5u,0.5u);z4=(3.5u,-0.5u);
z6=(0.5u,0u);z7=(6.5u,0u);z8=(2u,1.5u);z9=(2.5u,1.5u);z10=(5u,1.5u);

%creation de l'axe et des flèches
draw z0--z1;
drawarrow z8{left}..z6{down}; drawarrow z10{right}..z7{down};
draw z2+(0,-0.1u)--z2+(0,0.1u);

%le texte
label.bot(btex $0$ etex, z3);
label.top(btex $x_0$ etex, z4);
label.rt(btex signe de $a$ etex,z9); 

endfig;

beginfig(3);
numeric u;
u = 1cm;
z0=(0,0);z1=(7u,0);z9=(2.5u,0.5u);
%creation de l'axe et des flèches
draw z0--z1;

%le texte
label.rt(btex signe de $a$ etex,z9); 

endfig;



%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                (0.25)*(t**2)+(0.75)*t-1
enddef;
%============================================================================
                

beginfig(4);
path p; 
repere(0,0,-5,3,-2,2,0.5cm,1cm);
r_axes;
r_origine;
p = f_courbe(-5,2,100);
z0 = r_point(-4.2,fy(-4));
z1 = r_point(1.2,fy(1));
r_ppoint(-4,fy(-4));
r_ppoint(1,fy(1));
label.bot(btex $x_1$ etex, z0);
label.bot(btex $x_2$ etex, z1);
r_point_proj(-1.5,fy(-1.5));
z2 = r_point(-1.5,0);
label.top(btex $-\frac{b}{2a}$ etex, z2);
z3 = r_point(0,fy(-1.5));
label.rt(btex $f(-\frac{b}{2a})$ etex, z3);
draw p;
r_fin;
endfig;


%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                t**2-2*t+1
enddef;
%=============================================================================

beginfig(5);
                
			   
path p; 
repere(0,0,-1,3,-1,3,1cm,1cm);
r_axes;
r_origine;
p = f_courbe(-1,3,100);
z0 = r_point(1,fy(1));
r_ppoint(1,fy(1));
r_point_proj(1,fy(1));
label.bot(btex $x_0=-\frac{b}{2a}$ etex, z0);
draw p;
r_fin;
endfig;

%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                t**2+2*t+2
enddef;
%=============================================================================

beginfig(6);
			   
path p; 
repere(0,0,-2.5,1.5,-0.7,3.2,1cm,1cm);
r_axes;
r_origine;
p = f_courbe(-2.5,1.5,100);
r_point_proj(-1,fy(-1));
r_ppoint(-1,fy(-1));
z0=r_point(-1,0);
label.bot(btex $-\frac{b}{2a}$ etex, z0);
z1 = r_point(0,fy(-1));
label.rt(btex $f(-\frac{b}{2a})$ etex, z1);
draw p;
r_fin;
endfig;


%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                (-0.25)*(t**2)-(0.75)*t+1
enddef;
%=============================================================================

beginfig(7);

path p; 
repere(0,0,-5,3,-2,2,0.5cm,1cm);
r_axes;
r_origine;
p = f_courbe(-5,2,100);
z0 = r_point(-3.8,fy(-4));
z1 = r_point(0.8,fy(1));
r_ppoint(-4,fy(-4));
r_ppoint(1,fy(1));
label.bot(btex $x_1$ etex, z0);
label.bot(btex $x_2$ etex, z1);
r_point_proj(-1.5,fy(-1.5));
z2 = r_point(-1.5,0);
label.bot(btex $-\frac{b}{2a}$ etex, z2);
z3 = r_point(0,fy(-1.5));
label.rt(btex $f(-\frac{b}{2a})$ etex, z3);
draw p;
r_fin;
endfig;

%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                -(t**2)+2*t-1
enddef;
%=============================================================================

beginfig(8);
                
			   
path p; 
repere(0,0,-1,3,-3,1,1cm,1cm);
r_axes;
r_origine;
p = f_courbe(-1,3,100);
z0 = r_point(1,fy(1));
r_ppoint(1,fy(1));
r_point_proj(1,fy(1));
label.top(btex $x_0=-\frac{b}{2a}$ etex, z0);
draw p;
r_fin;
endfig;

%============================================================================
def fx(expr t) =
 			   t
enddef;
def fy(expr t) =
                -(t**2)-2*t-2
enddef;
%=============================================================================

beginfig(9);
			   
path p; 
repere(0,0,-2.5,1.5,-3.2,0.8,1cm,1cm);
r_axes;
r_origine;
p = f_courbe(-2.5,1.5,100);
r_point_proj(-1,fy(-1));
r_ppoint(-1,fy(-1));
z0=r_point(-1,0);
label.top(btex $-\frac{b}{2a}$ etex, z0);
z1 = r_point(0,fy(-1));
label.rt(btex $f(-\frac{b}{2a})$ etex, z1);
draw p;
r_fin;
endfig;







end