Interactive Quiz on Quadratic Function Graphs
2017-01-07 14:09
This interactive applet is a quiz tool for exploring quadratic function graphs. Users can generate random questions about parabola properties, such as the vertex, axis of symmetry, and intercepts. It dynamically visualizes parameter changes, helping students solidify their understanding of quadratic functions and their geometric representations.
In collections
代數
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.309.0" id="41eb478a-e381-45b1-92cc-7897f1f0f8bc" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1382" height="744" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1447178002894356" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="599,46,700,548" />
<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="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="1" visible="true" inframe="false" stylebar="true" location="1" size="1355" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<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" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" 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="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1355" height="573"/>
<coordSystem xZero="990.9999999999993" yZero="329.4999999999999" scale="50.00000000000007" yscale="49.99999999999987"/>
<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>
<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="line" label="c">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="1.0"/>
<bgColor r="255" g="239" b="213" alpha="255"/>
<layer val="0"/>
<labelOffset x="129" y="137"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="UpdateConstruction[] A:(-8,3) B:(-5,2) "/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<caption val="更新"/>
</element>
<expression label ="A" exp="(-8, 3)" type="point"/>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0" dynamicr="A ≠ C" dynamicg="A ≟ C" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelOffset x="4" y="-7"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-8.0" y="3.0" z="1.0"/>
<pointSize val="9"/>
<pointStyle val="0"/>
</element>
<expression label ="B" exp="(-5, 2)" type="point"/>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0" dynamicr="t ≠ 0" dynamicg="t ≟ 0" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-5.0" y="2.0" z="1.0"/>
<pointSize val="9"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="C_1"/>
</command>
<element type="point" label="C_1">
<show object="true" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="點c">
<show object="false" label="false"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="-1.379999999999998" y="0.9199999999999973" z="1.0"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="C_1" a1="xAxis"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Mirror">
<input a0="B" a1="f"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="C" exp="(Random[-3, 3], Random[-3, 3])" type="point" />
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="-3.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="h" exp="x(C)" />
<element type="numeric" label="h">
<value val="3.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="k" exp="y(C)" />
<element type="numeric" label="k">
<value val="-3.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="b" exp="(B * (-5, 2))" />
<element type="numeric" label="b">
<value val="29.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="g" exp="(B * (-5, 2))" />
<element type="numeric" label="g">
<value val="29.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Random">
<input a0="-2" a1="2"/>
<output a0="a"/>
</command>
<element type="numeric" label="a">
<value val="-1.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="d" exp="y = (a * (x - h)^(2)) + k" type="conic" />
<element type="conic" label="d">
<show object="false" label="false" ev="4"/>
<condition showObject="t^(2) + s^(2) ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<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="12.0" A3="0.0" A4="-3.0" A5="0.5"/>
<eqnStyle style="vertex"/>
</element>
<expression label="text2" exp=""1.移動A點到頂點 2.移動B點到函數圖形上""/>
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint x="-16.53000000000001" y="1.664999999999984" z="1.0"/>
</element>
<expression label="m" exp="x(B)" />
<element type="numeric" label="m">
<value val="-5.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="n" exp="y(B)" />
<element type="numeric" label="n">
<value val="2.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="t" exp="(a * (m - h)^(2)) + k - n" />
<element type="numeric" label="t">
<value val="-69.0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="i" exp="x = h" type="line" />
<element type="line" label="i">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="0.0" z="-3.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Mirror">
<input a0="B" a1="i"/>
<output a0="B'_1"/>
</command>
<element type="point" label="B'_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0" dynamicr="t ≠ 0" dynamicg="t ≟ 0" dynamicb="0" colorSpace="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="11.0" y="2.000000000000001" z="1.0"/>
<pointSize val="9"/>
<pointStyle val="0"/>
</element>
<command name="Midpoint">
<input a0="C" a1="A"/>
<output a0=""/>
</command>
<command name="Distance">
<input a0="A" a1="C"/>
<output a0="distanceAC"/>
</command>
<element type="numeric" label="distanceAC">
<value val="12.529964086141668"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Midpoint">
<input a0="A" a1="C"/>
<output a0=""/>
</command>
<expression label="文字AC" exp="Name[A] + (Name[C]) + " = " + distanceAC" />
<element type="text" label="文字AC">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="Midpoint[A, C]"/>
</element>
<command name="Distance">
<input a0="A" a1="C"/>
<output a0="s"/>
</command>
<element type="numeric" label="s">
<value val="12.529964086141668"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text1_1" exp=""y=" + (LaTeX[a]) + "(x-" + (LaTeX[h]) + ")^2+" + (LaTeX[k]) + """ />
<element type="text" label="text1_1">
<show object="true" label="false" ev="8"/>
<condition showObject="(h > 0) ∧ (k > 0) ∧ (a ≠ 0)"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-15.270000000000026" y="3.5600000000000036" z="1.0"/>
</element>
<expression label="text1_3" exp=""y= " + (LaTeX[a]) + "(x-" + (LaTeX[h]) + " )^2-" + (LaTeX[(-k)]) + """ />
<element type="text" label="text1_3">
<show object="true" label="false" ev="8"/>
<condition showObject="(h > 0) ∧ (k < 0) ∧ (a ≠ 0)"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-15.279999999999964" y="3.450000000000007" z="1.0"/>
</element>
<expression label="text1" exp=""y=" + (LaTeX[a]) + "(x+" + (LaTeX[(-h)]) + ")^2+" + (LaTeX[k]) + """ />
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<condition showObject="(h < 0) ∧ (k > 0) ∧ (a ≠ 0)"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-14.999999999999966" y="3.430000000000007" z="1.0"/>
</element>
<expression label="text3_1" exp=""y=" + (LaTeX[a]) + "(x+" + (LaTeX[(-h)]) + ")^2-" + (LaTeX[(-k)]) + """ />
<element type="text" label="text3_1">
<show object="true" label="true" ev="8"/>
<condition showObject="(h < 0) ∧ (k < 0) ∧ (a ≠ 0)"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-14.339999999999966" y="3.450000000000007" z="1.0"/>
</element>
<expression label="text3" exp=""恭喜答對了""/>
<element type="text" label="text3">
<show object="true" label="true" ev="40"/>
<condition showObject="t^(2) + s^(2) ≟ 0"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="8.0" size="84" style="1"/>
<startPoint x="-18.439999999999962" y="-2.6900000000000093" z="1.0"/>
</element>
</construction>
</geogebra>