二次不等式△>0且a>0示例
2020-03-09 23:54
本示例展示了二次不等式△>0且a>0的解集在坐标系中的图形表示，通过GeoGebra软件进行动态演示，帮助理解二次不等式的解集特性。
所属专题
中职数学GeoGebra互动教学资源库
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="w" id="73e2a821-714d-4e4a-878a-b1b33e2211f7" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1334" height="539" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.14992503748125938" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 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="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" 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="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="552" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1126" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="200" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" 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="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" 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="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1126" height="539"/>
<coordSystem xZero="288" yZero="312.00000000000017" scale="50.00000000000002" yscale="50.00000000000003"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="x_1">
<value val="2"/>
<show object="true" label="true"/>
<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" x="55" y="48" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="3" type="0" playing="false"/>
</element>
<element type="numeric" label="x_2">
<value val="-1"/>
<show object="true" label="true"/>
<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" x="57" y="97" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Point">
<input a0="y = 0"/>
<output a0="X"/>
</command>
<element type="point" label="X">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<auxiliary val="true"/>
<ggbscript onUpdate="txja="x-a="xx If[x_1>=0,"-"x_1,"+"abs(x_1)]"="xja If[xja>0,">0",If[xja<0,"<0"]]
txjb="x-b="xx If[x_2>=0,"-"x_2,"+"abs(x_2)]"="xjb If[xjb>0,">0",If[xjb<0,"<0"]]
hsjxs="函数解析式：y=(x"If[x_1>=0,"-"x_1,"+"abs(x_1)]")(x"If[x_2>=0,"-"x_2,"+"abs(x_2)]")"
bdsdyl="不等式：(x"If[x_1>=0,"-"x_1,"+"abs(x_1)]")(x"If[x_2>=0,"-"x_2,"+"abs(x_2)]")>0\\解集为："If[x_2>x_1,"(-∞,"x_1")∪("x_2",+∞)","(-∞,"x_2")∪("x_1",+∞)"]
bdsxyl="不等式：(x"If[x_1>=0,"-"x_1,"+"abs(x_1)]")(x"If[x_2>=0,"-"x_2,"+"abs(x_2)]")<0\\解集为："If[x_1==x_2,"∅",If[x_2>x_1,"("x_1","x_2")","("x_2","x_1")"]]
"/>
<coords x="0.72" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="x"/>
</element>
<expression label="xx" exp="x(X)" />
<element type="numeric" label="xx">
<value val="0.72"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<caption val="x"/>
</element>
<expression label="xjb" exp="xx - x_2" />
<element type="numeric" label="xjb">
<value val="1.72"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<auxiliary val="true"/>
</element>
<expression label="xja" exp="xx - x_1" />
<element type="numeric" label="xja">
<value val="-1.28"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<auxiliary val="true"/>
</element>
<expression label="f" exp="f(x) = ((x - x_1) * (x - x_2))" />
<element type="function" label="f">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="20" typeHidden="1" opacity="178"/>
</element>
<expression label="A" exp="(xx, ((xx - x_1) * (xx - x_2)))" type="point" />
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0.72" y="-2.2016" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="txjb" exp="((((("x-b=" * xx) * If[x_2 ≥ 0, ("-" * x_2), ("+" * abs(x_2))]) * "=") * xjb) * If[xjb > 0, ">0", If[xjb < 0, "<0"]])" />
<element type="text" label="txjb">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<auxiliary val="true"/>
<startPoint x="0.7199999999999998" y="4.579999999999999" z="1"/>
</element>
<expression label="B" exp="(x_1, 0)" type="point" />
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-23" y="29"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="2" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="2"/>
</element>
<expression label="C" exp="(x_2, 0)" type="point" />
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="12" y="23"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-1" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="2"/>
</element>
<command name="Segment">
<input a0="(Min[x_1, x_2] - 5, 0.3)" a1="(Min[x_1, x_2], 0.3)"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="5" z="-1.4999999999999998"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(Min[x_1, x_2], 0)" a1="(Min[x_1, x_2], 0.3)"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.3" y="0" z="-0.3"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(Max[x_1, x_2], 0.3)" a1="(Max[x_1, x_2] + 5, 0.3)"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="5" z="-1.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(Max[x_1, x_2], 0)" a1="(Max[x_1, x_2], 0.3)"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.3" y="0" z="0.6"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(Min[x_1, x_2], -0.3)" a1="(Max[x_1, x_2], -0.3)"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="51" b="153" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="3" z="0.8999999999999999"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(Min[x_1, x_2], -0.3)" a1="(Min[x_1, x_2], 0)"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="51" b="153" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.3" y="0" z="-0.3"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(Max[x_1, x_2], -0.3)" a1="(Max[x_1, x_2], 0)"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="51" b="153" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.3" y="0" z="0.6"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="bdsdyl" exp="((((("不等式：(x" * If[x_1 ≥ 0, ("-" * x_1), ("+" * abs(x_1))]) * ")(x") * If[x_2 ≥ 0, ("-" * x_2), ("+" * abs(x_2))]) * ")>0\\解集为：") * If[x_2 > x_1, (((("(-∞," * x_1) * ")∪(") * x_2) * ",+∞)"), (((("(-∞," * x_2) * ")∪(") * x_1) * ",+∞)")])" />
<element type="text" label="bdsdyl">
<show object="true" label="true" ev="8"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="1"/>
<startPoint x="3.0399999999999996" y="2.6399999999999983" z="1"/>
</element>
<expression label="bdsxyl" exp="((((("不等式：(x" * If[x_1 ≥ 0, ("-" * x_1), ("+" * abs(x_1))]) * ")(x") * If[x_2 ≥ 0, ("-" * x_2), ("+" * abs(x_2))]) * ")<0\\解集为：") * If[x_1 ≟ x_2, "∅", If[x_2 > x_1, (((("(" * x_1) * ",") * x_2) * ")"), (((("(" * x_2) * ",") * x_1) * ")")]])" />
<element type="text" label="bdsxyl">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="51" b="153" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="1"/>
<startPoint x="3.0599999999999996" y="-2.059999999999999" z="1"/>
</element>
<expression label="txja" exp="((((("x-a=" * xx) * If[x_1 ≥ 0, ("-" * x_1), ("+" * abs(x_1))]) * "=") * xja) * If[xja > 0, ">0", If[xja < 0, "<0"]])" />
<element type="text" label="txja">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<auxiliary val="true"/>
<startPoint x="0.7200000000000017" y="5.199999999999998" z="1"/>
</element>
<expression label="hsjxs" exp="(((("函数解析式：y=(x" * If[x_1 ≥ 0, ("-" * x_1), ("+" * abs(x_1))]) * ")(x") * If[x_2 ≥ 0, ("-" * x_2), ("+" * abs(x_2))]) * ")")" />
<element type="text" label="hsjxs">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="1"/>
<startPoint x="0.3599999999999999" y="6.039999999999997" z="1"/>
</element>
</construction>
</geogebra>