Mathematical curves with calculated crosspoints

Application in jscript or other technique to draw on canvas or other object 1-6 parabolic curves calculated from formula like y=ax^2 +bx+c where a b and c are taken from xml file and calculated cross-points and publish cross-point coordinates under drawing, then it must be possible to export and print out. Task can be done on java or cocoa or python as well. Description is similar but not exactly what must be done. Best bidders will receive full technical description and test to prove you are capable to do the job. PM me if you want full description.