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Question: Draw a line through all maxima

Question:Draw a line through all maxima

qwertz 22 Maple 13
coordinates plot graph student
June 27 2010
0

I have a family of functions characterized by

f:=x^2+b*x+b*3;

I plotted some of them:

graph1:=x->subs(b=0,f):
graph2:=x->subs(b=2,f):
graph3:=x->subs(b=4,f):
plot([graph1(x),graph2(x),graph3(x)],x=-10..3,y=-5..15);

And now I want to draw a line through all maxima into the same diagram. The maxima have the coordinates (-1/2*b | -1/4*b^2+3*b). I managed to create a pointplot:

with(plots):
pointplot({seq([-1/2*b, -1/4*b^2+3*b], b = 0 .. 13)});

However these are just points and ---more importantly--- not in the same diagram as the functions. Some ideas?
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