二次函数左右x值差
2017-01-18 02:29
本范例演示了二次函数（抛物线）中，关于对称轴对称的两点其横坐标（x值）之差的计算与几何意义。通过构造直角三角形和辅助线，直观展示了抛物线上特定两点间的水平距离，帮助理解二次函数的对称性及其在解析几何中的应用。
所属专题
二次函数
GeoGebra 画板及绘图内容加载中，请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.313.0" id="f29820e0-51df-4bf3-af2b-ad1c8e03c786" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1382" height="784" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.7800289435600579" orientation="1" />
<pane location="0" divider="0.34876989869753977" orientation="1" />
</panes>
<views>
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3,3" size="196" window="100,100,250,400" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3,3" size="482" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="3,1" size="591" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="true" inframe="false" stylebar="true" location="1" size="272" window="588,69,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="482" height="507"/>
<coordSystem xZero="153.6711875000003" yZero="410.30156249999953" scale="60.60312500000002" yscale="60.60312500000001"/>
<evSettings axes="true" 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="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="591" height="540"/>
<coordSystem xZero="215.0000000000001" yZero="315.00000000000006" scale="50.00000000000003" yscale="50.00000000000003"/>
<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"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="1.0"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="50.0" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="h1">
<value val="0.0"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="30.0" y="109.0" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="h2">
<value val="3.0"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200.0" x="32.0" y="156.0" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""y=(x-h_1)^2""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<objColor r="127" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="-2.2056814314443365" y="-0.3085391636157434" z="1.0"/>
</element>
<expression label="text1_1" exp=""y=(x-h_2)^2""/>
<element type="text" label="text1_1">
<show object="true" label="false" ev="40"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="1.6555055948022463" y="-0.34154076213067464" z="1.0"/>
</element>
<expression label="c" exp="y = (a * (x - h1)^(2))" type="conic" />
<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="127" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="0.0" y0="1.0" z0="1.0" x1="-1.0" y1="0.0" z1="1.0"/>
<matrix A0="-1.0" A1="0.0" A2="0.0" A3="0.0" A4="0.0" A5="0.5"/>
<eqnStyle style="explicit"/>
</element>
<expression label="d" exp="y = (a * (x - h2)^(2))" type="conic" />
<element type="conic" label="d">
<show object="true" label="false" ev="8"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="0.0" y0="1.0" z0="1.0" x1="-1.0" y1="0.0" z1="1.0"/>
<matrix A0="-1.0" A1="0.0" A2="-9.0" A3="0.0" A4="3.0" A5="0.5"/>
<eqnStyle style="explicit"/>
</element>
</construction>
</geogebra>