Algebra/Unit 4 Quiz 1/Objective 2c
x-intercepts 1
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»State«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mi»intercepts«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»following«/mi»«mo»§#160;«/mo»«mi»quadratic«/mi»«mo»§#160;«/mo»«mi»function«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»q«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Write«/mi»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»as«/mi»«mo»§#160;«/mo»«mi»ordered«/mi»«mo»§#160;«/mo»«mi»pairs«/mi»«mo».«/mo»«/math»]]>
1.0000000
0.3333333
0
0
x-intercept 1 = (#x)x-intercept 2 = (#y)]]>
x-intercept 1 = (#y)x-intercept 2 = (#x)]]>
x-intercept 1 = (#g)x-intercept 2 = (#h)]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Y«/mi»«mi»o«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»n«/mi»«mi»s«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»T«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»-«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»c«/mi»«mi»e«/mi»«mi»p«/mi»«mi»t«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»y«/mi»«mo»)«/mo»«/math»]]>
x-intercept 1 = (#h)x-intercept 2 = (#g)]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Y«/mi»«mi»o«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»n«/mi»«mi»s«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»T«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»-«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»c«/mi»«mi»e«/mi»«mi»p«/mi»«mi»t«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»y«/mi»«mo»)«/mo»«/math»]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>p</mi><mo>≠</mo><mi>q</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>(</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="3" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="4"></correctAnswer><correctAnswer id="5"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="check_simplified" correctAnswer="1"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="check_simplified" correctAnswer="2"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="equivalent_symbolic" correctAnswer="2"/><assertion name="check_simplified" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="3"/><assertion name="equivalent_symbolic" correctAnswer="3"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
x-intercepts 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»State«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mi»intercepts«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»following«/mi»«mo»§#160;«/mo»«mi»quadratic«/mi»«mo»§#160;«/mo»«mi»function«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»q«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Write«/mi»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»as«/mi»«mo»§#160;«/mo»«mi»ordered«/mi»«mo»§#160;«/mo»«mi»pairs«/mi»«mo».«/mo»«/math»]]>
1.0000000
0.3333333
0
0
x-intercept 1 = (#x)x-intercept 2 = (#y)]]>
x-intercept 1 = (#y)x-intercept 2 = (#x)]]>
x-intercept 1 = (#g)x-intercept 2 = (#h)]]>
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x-intercept 1 = (#h)x-intercept 2 = (#g)]]>
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<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>p</mi><mo>≠</mo><mi>q</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>(</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="3" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="4"></correctAnswer><correctAnswer id="5"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="check_simplified" correctAnswer="1"/><assertion name="check_simplified" correctAnswer="2"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="equivalent_symbolic" correctAnswer="2"/><assertion name="check_simplified" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="3"/><assertion name="equivalent_symbolic" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
x-intercepts 3
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»State«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mi»intercepts«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»following«/mi»«mo»§#160;«/mo»«mi»quadratic«/mi»«mo»§#160;«/mo»«mi»function«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»q«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Write«/mi»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»as«/mi»«mo»§#160;«/mo»«mi»ordered«/mi»«mo»§#160;«/mo»«mi»pairs«/mi»«mo».«/mo»«/math»]]>
1.0000000
0.3333333
0
0
x-intercept 1 = (#x)x-intercept 2 = (#y)]]>
x-intercept 1 = (#y)x-intercept 2 = (#x)]]>
x-intercept 1 = (#g)x-intercept 2 = (#h)]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Y«/mi»«mi»o«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»n«/mi»«mi»s«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»T«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»-«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»c«/mi»«mi»e«/mi»«mi»p«/mi»«mi»t«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»y«/mi»«mo»)«/mo»«/math»]]>
x-intercept 1 = (#h)x-intercept 2 = (#g)]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Y«/mi»«mi»o«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»n«/mi»«mi»s«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»T«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»-«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»c«/mi»«mi»e«/mi»«mi»p«/mi»«mi»t«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»y«/mi»«mo»)«/mo»«/math»]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>p</mi><mo>≠</mo><mi>q</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>(</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="3" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="4"></correctAnswer><correctAnswer id="5"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="check_simplified" correctAnswer="1"/><assertion name="check_simplified" correctAnswer="2"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="equivalent_symbolic" correctAnswer="2"/><assertion name="check_simplified" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="3"/><assertion name="equivalent_symbolic" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
x-intercepts 4
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»State«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mi»intercepts«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»following«/mi»«mo»§#160;«/mo»«mi»quadratic«/mi»«mo»§#160;«/mo»«mi»function«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»q«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»Write«/mi»«mo»§#160;«/mo»«mi»your«/mi»«mo»§#160;«/mo»«mi»answer«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»as«/mi»«mo»§#160;«/mo»«mi»ordered«/mi»«mo»§#160;«/mo»«mi»pairs«/mi»«mo».«/mo»«/math»]]>
1.0000000
0.3333333
0
0
x-intercept 1 = (#x)x-intercept 2 = (#y)]]>
x-intercept 1 = (#y)x-intercept 2 = (#x)]]>
x-intercept 1 = (#g)x-intercept 2 = (#h)]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Y«/mi»«mi»o«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»n«/mi»«mi»s«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»T«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»-«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»c«/mi»«mi»e«/mi»«mi»p«/mi»«mi»t«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»y«/mi»«mo»)«/mo»«/math»]]>
x-intercept 1 = (#h)x-intercept 2 = (#g)]]>
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»Y«/mi»«mi»o«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»h«/mi»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»p«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»t«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»n«/mi»«mi»s«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»T«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»r«/mi»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»-«/mo»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»c«/mi»«mi»e«/mi»«mi»p«/mi»«mi»t«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»y«/mi»«mo»)«/mo»«/math»]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>p</mi><mo>≠</mo><mi>q</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>(</mo><mi>q</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>y</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>x</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="3" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>h</mi><mo>)</mo><mspace linebreak="newline"/><mi>x</mi><mo>-</mo><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>t</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mo>#</mo><mi>g</mi><mo>)</mo></math>]]></correctAnswer><correctAnswer id="4"></correctAnswer><correctAnswer id="5"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="check_simplified" correctAnswer="1"/><assertion name="check_simplified" correctAnswer="2"/><assertion name="syntax_expression" correctAnswer="2"/><assertion name="equivalent_symbolic" correctAnswer="2"/><assertion name="check_simplified" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="3"/><assertion name="equivalent_symbolic" correctAnswer="3"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>