Parabolic Segment Area
2016-04-15 01:01
This example demonstrates how to draw a parabolic segment area using the PathParameter command in GeoGebra. By constructing a parabola, lines, and intersection points, and combining the Sequence and Polygon commands, it dynamically generates and fills the parabolic segment, providing an intuitive visualization of region construction in quadratic functions and coordinate geometry.
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<window width="900" height="600" />
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<pane location="0" divider="0.1111111111111111" orientation="1" />
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<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<consProtColumns col0="true" col1="true" col2="false" col3="false" col4="true" col5="false" col6="false" col7="false"/>
<consProtocol useColors="false" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="455" height="598"/>
<coordSystem xZero="199.74547656208276" yZero="383.1306162995495" scale="59.52748968872714" yscale="59.52748968872703"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.1640939220096667" y="-0.09652719611633019" z="1"/>
<pointSize val="5"/>
<pointStyle val="5"/>
</element>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.346280193369199" y="1.1989680131306344" z="1"/>
<pointSize val="5"/>
<pointStyle val="5"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="a"/>
</command>
<element type="line" label="a">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.2954952092469645" y="3.5103741153788657" z="-1.1692315284001678"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
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<element type="point" label="C">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.10354117521047979" y="1.6725899175865138" z="1"/>
<pointSize val="3"/>
<pointStyle val="1"/>
</element>
<command name="Parabola">
<input a0="C" a1="a"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="-0.3462228699323803" y0="0.9381522927199966" z0="1.0" x1="-0.9381522927199966" y1="-0.3462228699323803" z1="1.0"/>
<matrix A0="12.322726429921953" A1="1.6783078371818363" A2="37.95169144561388" A3="4.5476728491378715" A4="-2.964417385721048" A5="-19.31354865876027"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.6716788106040172" y="1.6095923260755043" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1.802190593958041" y="4.6778965572020965" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="E"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-3.068304231126592" y="3.473869404562058" z="-10.720732703032546"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="PathParameter">
<input a0="D"/>
<output a0="t1"/>
</command>
<element type="numeric" label="t1">
<value val="0.790097324874511"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="PathParameter">
<input a0="E"/>
<output a0="t2"/>
</command>
<element type="numeric" label="t2">
<value val="0.15834552689740228"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Min">
<input a0="t1" a1="t2"/>
<output a0="s1"/>
</command>
<element type="numeric" label="s1">
<value val="0.15834552689740228"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Max">
<input a0="t1" a1="t2"/>
<output a0="s2"/>
</command>
<element type="numeric" label="s2">
<value val="0.790097324874511"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Sequence">
<input a0="Point[c, s]" a1="s" a2="s1" a3="s2" a4="(s2 - s1) / 50"/>
<output a0="points"/>
</command>
<element type="list" label="points">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Polygon">
<input a0="points"/>
<output a0="poly1"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.55"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
</construction>
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