(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 155023, 7053]*) (*NotebookOutlinePosition[ 156078, 7089]*) (* CellTagsIndexPosition[ 156034, 7085]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{Cell[TextData["Parabola Plotter"], "Title", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Marion Harding"], "Subtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["1994 ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago", FontSlant->"Plain"], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago"], StyleBox[" Workshop", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago", FontSlant->"Plain"] }], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[StyleBox[ "By definition, a parabola is the set of all points in a plane that are the \ same distance from a fixed point and a fixed line in the plane. 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StyleBox[ "The following code finds the focus and the directrix of any parabola. One \ can enter the coefficients, a, b, and c, and produce a graph showing the \ focus and directrix. Entering the same a, b, and c again, the vertex, focus, \ and directrix are given. (Some comments about the code are included.)\n", Evaluatable->False, AspectRatioFixed->True, FontFamily->"CalcMath", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"CalcMath"] }], "Subsection", Evaluatable->False, AspectRatioFixed->True, FontFamily->"CalcMath"], Cell[TextData[ "Clear[a,b,c,vy,vx,p1,focus]\n\n(*This program graphs a parabola, its\n \ focus, and its directrix with any \n a, b, and c. To enter a, b, c, \n \ type Parabolamaker[] and enter.*) \n\nParabolamaker[]:=\n\n\ Module[{a,b,c,vy,vx,p1,focus,f},\n\na=Input[\"Enter in a\"];\nb=Input[\"Enter \ in b\"];\nc=Input[\"Enter in c\"];\n\nf[x_] = a x^2 + b x + c;\n\nvx = -b/(2 \ a);\n\nvy = a (vx)^2 + b (vx) + c;\n(*This graphs the directrix*)\np1=\nPlot[\ \n\n(* The If statement takes the first argument if true,\n and the second \ argument if false*)\n \n{If[a>0,\n\n\tvy - Abs[1/(4a)],\n\tvy + \ Abs[1/(4a)]],\n\t\n \tf[x]},\n\n(*The domain is one unit each side of the \ vertex*)\n\n{x,vx-1,vx+1},\n\tPlotLabel->StringForm[\"y = ``\",f[x]],\n \ PlotStyle->{{RGBColor[0,1,0],Thickness[0.015]},\n\t \ {RGBColor[0,0,1],Thickness[0.01]}},\n \n (*The range is 3/Abs[4a] above and \ below the vertex*)\n \n PlotRange->{vy - 3/Abs[4a],vy + 3/Abs[4a]}, \ AspectRatio->1,\n DisplayFunction->Identity];\n\t \nfocus=\n\ Graphics[{PointSize[0.025],RGBColor[0,1,0],\nIf[a>0,Point[{vx,vy+1/(4 \ a)}],Point[{vx,vy-Abs[1/(4 a)]}]]}];\n\n\n\ Show[p1,focus,DisplayFunction->$DisplayFunction];\n\n\n]; (*the Module \ Parabola maker ends*)\n"], "Input", Editable->False, InitializationCell->True, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "coef[a_,b_,c_]:=\n\n(vx=-b/(2a);\n\tvy=a (-b/(2 a))^2 + b (-b/(2 a)) + c;\n\ \n\nPrint[StringForm[\"The ", Editable->False, InitializationCell->True, AspectRatioFixed->True], StyleBox["vertex", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox[" is: ", Editable->False, InitializationCell->True, AspectRatioFixed->True], StyleBox["``. 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