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Textbook is \ licensed under CC BY 4.0 via Commons\n\t\t\t\t\t\tDownload for free at ", FontSize->12], "http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/\ Preface", StyleBox[" \n", FontSize->12] }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 0}, CellChangeTimes->{{3.649088495646085*^9, 3.6490886606035194`*^9}, { 3.649088769325738*^9, 3.649088770198788*^9}, {3.6490888913367167`*^9, 3.6490889736564255`*^9}, 3.6490890056672564`*^9, {3.649090412749737*^9, 3.649090434975008*^9}, {3.649090513529501*^9, 3.649090530170453*^9}, { 3.6490905629713287`*^9, 3.6490905965002465`*^9}, 3.649090770501199*^9}, TextAlignment->Right, FontSize->10], Cell[TextData[{ StyleBox["Example 1:", FontVariations->{"Underline"->True}], " Use the interactive frame below to test your graphing skills. The word \ \[OpenCurlyDoubleQuote]True\[CloseCurlyDoubleQuote] will appear when you move \ each point to its correct place on the complex plane." }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 0}, CellChangeTimes->{{3.6490907942495575`*^9, 3.64909081877196*^9}, { 3.6490909054139156`*^9, 3.64909095951001*^9}}, FontFamily->"Calibri", FontSize->24] }, Open ]], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`help$$ = True, $CellContext`n$$ = 7, $CellContext`nn$$ = {{5, -5}, {6, 2}, {3, 7}, {8, 1}, {0, 3}, {-3, -8}, {2, -4}}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`n$$], 7, "number of points"}, 1, 15, 1}, {{ Hold[$CellContext`help$$], True, "show grid lines"}, {False, True}}, {{ Hold[$CellContext`nn$$], {{5, -3}, {-6, -7}, {-2, 4}, {4, 1}, {-3, -4}, {7, 8}, {-8, 2}}}, {-9, -9}, {9, 9}, {1, 1}}, { Hold[ Style["Move the points to their given complex numbers!"]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = { 450., {146., 154.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`n$1101$$ = 0, $CellContext`help$1102$$ = False, $CellContext`nn$1103$$ = {0, 0}}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`help$$ = True, $CellContext`n$$ = 7, $CellContext`nn$$ = $CellContext`RandomKsublist[ $CellContext`set2[9], 7]}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$1101$$, 0], Hold[$CellContext`help$$, $CellContext`help$1102$$, False], Hold[$CellContext`nn$$, $CellContext`nn$1103$$, {0, 0}]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> With[{$CellContext`st1$ = $CellContext`RandomKsublist[ $CellContext`set2[ 9], $CellContext`n$$], $CellContext`st$ = \ $CellContext`RandomKsublist[ $CellContext`set2[9], $CellContext`n$$]}, With[{$CellContext`st1C$ = Map[$CellContext`ToComplex, $CellContext`st1$]}, $CellContext`nn$$ = \ $CellContext`st$; 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" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 0}, CellChangeTimes->{{3.6490907942495575`*^9, 3.64909081877196*^9}, { 3.6490909054139156`*^9, 3.64909095951001*^9}, {3.6625572531037283`*^9, 3.662557293135507*^9}, {3.6625574862592645`*^9, 3.6625574901463237`*^9}, { 3.662557773887947*^9, 3.662557873813713*^9}, {3.6625579230820203`*^9, 3.662557938906976*^9}, {3.662558237215726*^9, 3.66255823722073*^9}}, FontFamily->"Calibri", FontSize->24], Cell[TextData[{ "\ta.\tShow algebraically that both f and -f have real zeros at x = 2 \ \[PlusMinus] ", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]], FormatType->"TraditionalForm"], ". Notice that the zeros are represented by the ", StyleBox["red", FontColor->RGBColor[1, 0, 0]], " dots on the x-axis." }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 0}, CellChangeTimes->{{3.6490907942495575`*^9, 3.64909081877196*^9}, { 3.6490909054139156`*^9, 3.64909095951001*^9}, {3.6625572531037283`*^9, 3.662557293135507*^9}, {3.6625574862592645`*^9, 3.6625574901463237`*^9}, { 3.662557773887947*^9, 3.662557873813713*^9}, {3.6625579230820203`*^9, 3.662557938906976*^9}, {3.662558237215726*^9, 3.6625582573392744`*^9}, { 3.662558454607044*^9, 3.662558514557386*^9}, {3.6625587785871735`*^9, 3.6625588169509416`*^9}}, FontFamily->"Calibri", FontSize->24], Cell[TextData[{ "\tb.\tUse the vertical translation slider to graph g(x) = ", Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], RowBox[{"2", " "}]], TraditionalForm]], FormatType->"TraditionalForm"], "+ 4. Show algebraically that g (and its reflection about the x-axis, -g) \ has complex zeros at x = 2 \[PlusMinus] 2", StyleBox[" i", FontSlant->"Italic"], ". Notice that since the quadratic never intersects the x-axis, the ", StyleBox["red", FontColor->RGBColor[1, 0, 0]], " dots representing the zeros have now moved into the complex plane. " }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 0}, CellChangeTimes->{{3.6490907942495575`*^9, 3.64909081877196*^9}, { 3.6490909054139156`*^9, 3.64909095951001*^9}, {3.6625572531037283`*^9, 3.662557293135507*^9}, {3.6625574862592645`*^9, 3.6625574901463237`*^9}, { 3.662557773887947*^9, 3.662557873813713*^9}, {3.6625579230820203`*^9, 3.662557938906976*^9}, {3.662558237215726*^9, 3.6625582573392744`*^9}, { 3.662558454607044*^9, 3.6625584918721647`*^9}, {3.662558537152362*^9, 3.6625585692941275`*^9}, {3.6625586338815894`*^9, 3.662558771259317*^9}, { 3.6625588229529195`*^9, 3.662558868200449*^9}, {3.6625596363713737`*^9, 3.662559653539688*^9}}, FontFamily->"Calibri", FontSize->24], Cell[TextData[{ "\tc.\tCreate another quadratic function h(x) that has only 1 real zero. \ This means that both ", StyleBox["red", FontColor->RGBColor[1, 0, 0]], " dots lie on the ", StyleBox["same", FontSlant->"Italic"], " x-intercept!" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 0}, CellChangeTimes->{{3.6490907942495575`*^9, 3.64909081877196*^9}, { 3.6490909054139156`*^9, 3.64909095951001*^9}, {3.6625572531037283`*^9, 3.662557293135507*^9}, {3.6625574862592645`*^9, 3.6625574901463237`*^9}, { 3.662557773887947*^9, 3.662557873813713*^9}, {3.6625579230820203`*^9, 3.662557938906976*^9}, {3.662558237215726*^9, 3.6625582573392744`*^9}, { 3.662558454607044*^9, 3.6625584918721647`*^9}, {3.662558537152362*^9, 3.6625585692941275`*^9}, {3.6625586338815894`*^9, 3.662558771259317*^9}, { 3.6625588229529195`*^9, 3.6625589925607815`*^9}, {3.6625595236423173`*^9, 3.662559539958358*^9}}, FontFamily->"Calibri", FontSize->24], Cell[TextData[{ "\td.\tCreate a different quadratic function that (i) opens downward, (ii) \ is wider than the parent function y = ", Cell[BoxData[ FormBox[ SuperscriptBox["x", "2"], TraditionalForm]], FormatType->"TraditionalForm"], " and has 2 distinct complex zeros. 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