Exploring the Graph of Quadratic Function y=x²+a

2012-06-02 01:57

This example demonstrates the graph of the quadratic function y=x²+a and its dynamic changes as the parameter a varies. By adjusting the parameter a, users can intuitively observe the vertical translation of the parabola in the coordinate system. This interactive tool helps students deeply understand the effect of the constant term on the position of the quadratic function's graph, mastering the b

#function #graphing #slider #transform

<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.0" id="19ab533c-ab5b-4306-9242-172b7a8736a0" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
	<window width="1942" height="1046" />
	<perspectives>
<perspective id="tmp">
	<panes>
		<pane location="" divider="0.13027806385169927" orientation="1" />
	</panes>
	<views>
		<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="200" window="0,0,400,400" />
		<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1920" window="0,0,400,400" />
		<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="0,0,200,400" />
		<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
		<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
		<view id="64" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
	</views>
	<toolbar show="true" items="0 39 59 || 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" />
	<input show="true" cmd="true" top="false" />
</perspective>
	</perspectives>
	<labelingStyle val="3"/>
	
	<graphicsSettings javaLatexFonts="false"/>
	<consProtColumns col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
	<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
	<size width="1920" height="853"/>
	<coordSystem xZero="559.0" yZero="542.0" scale="50.0" yscale="50.00000000000002"/>
	<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" 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="10"/>
	<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"/>
	<decimals val="2"/>
	<angleUnit val="degree"/>
	<algebraStyle val="0"/>
	<coordStyle val="0"/>
	<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
	<value val="1.5"/>
	<show object="true" label="true"/>
	<objColor r="51" g="51" b="255" alpha="0.1"/>
	<layer val="0"/>
	<labelMode val="1"/>
	<slider min="0" max="6" absoluteScreenLocation="true" width="200.0" x="807.0" y="70.0" fixed="false" horizontal="true"/>
	<lineStyle thickness="4" type="0" typeHidden="1"/>
	<animation step="0.5" speed="1" type="0" playing="false"/>
</element>
<expression label="c" exp="y = x^(2) + a" type="conic" />
<element type="conic" label="c">
	<show object="true" label="false"/>
	<objColor r="51" g="0" b="204" 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="-1.5" A3="0.0" A4="0.0" A5="0.5"/>
	<eqnStyle style="explicit"/>
</element>
<element type="conic" label="d">
	<show object="true" label="false"/>
	<objColor r="255" g="0" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<animation step="0.1" speed="1" type="0" playing="false"/>
	<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="文字1" exp="&quot;y=x²+a(a&gt;0)的圖形是由y=x²的圖形向上平移a個單位而得。&quot;"/>
<element type="text" label="文字1">
	<show object="true" label="false"/>
	<objColor r="0" g="0" b="204" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	
	<startPoint x="-10.82" y="0.8200000000000004" z="1.0"/>
</element>
<expression label="文字2" exp="&quot;y=x²&quot;"/>
<element type="text" label="文字2">
	<show object="true" label="false"/>
	<objColor r="255" g="0" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	
	<startPoint x="1.7" y="2.34" z="1.0"/>
</element>
<expression label="文字3" exp="&quot;y=x²+a&quot;"/>
<element type="text" label="文字3">
	<show object="true" label="false"/>
	<objColor r="204" g="0" b="204" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	
	<startPoint exp="(0, a + 1)"/>
</element>
<expression label="text1" exp="&quot;2012.6.2阿培製&quot;"/>
<element type="text" label="text1">
	<show object="true" label="false"/>
	<condition showObject="a &gt; 2"/>
	<objColor r="102" g="102" b="255" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	
	<startPoint x="5.78" y="0.9999999999999996" z="1.0"/>
</element>
</construction>
</geogebra>

<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.0" id="19ab533c-ab5b-4306-9242-172b7a8736a0"  xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
	<window width="1942" height="1046" />
	<perspectives>
<perspective id="tmp">
	<panes>
		<pane location="" divider="0.13027806385169927" orientation="1" />
	</panes>
	<views>
		<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="200" window="0,0,400,400" />
		<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1920" window="0,0,400,400" />
		<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="0,0,200,400" />
		<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
		<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
		<view id="64" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
	</views>
	<toolbar show="true" items="0 39 59 || 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" />
	<input show="true" cmd="true" top="false" />
</perspective>
	</perspectives>
	<labelingStyle  val="3"/>
	<font  size="12"/>
	<graphicsSettings javaLatexFonts="false"/>
	<consProtColumns  col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
	<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
	<size  width="1920" height="853"/>
	<coordSystem xZero="559.0" yZero="542.0" scale="50.0" yscale="50.00000000000002"/>
	<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" 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="10"/>
	<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"/>
	<decimals val="2"/>
	<angleUnit val="degree"/>
	<algebraStyle val="0"/>
	<coordStyle val="0"/>
	<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
	<value val="1.5"/>
	<show object="true" label="true"/>
	<objColor r="51" g="51" b="255" alpha="0.1"/>
	<layer val="0"/>
	<labelMode val="1"/>
	<slider min="0" max="6" absoluteScreenLocation="true" width="200.0" x="807.0" y="70.0" fixed="false" horizontal="true"/>
	<lineStyle thickness="4" type="0" typeHidden="1"/>
	<animation step="0.5" speed="1" type="0" playing="false"/>
</element>
<expression label="c" exp="y = x^(2) + a" type="conic" />
<element type="conic" label="c">
	<show object="true" label="false"/>
	<objColor r="51" g="0" b="204" 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="-1.5" A3="0.0" A4="0.0" A5="0.5"/>
	<eqnStyle style="explicit"/>
</element>
<element type="conic" label="d">
	<show object="true" label="false"/>
	<objColor r="255" g="0" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<animation step="0.1" speed="1" type="0" playing="false"/>
	<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="文字1" exp="&quot;y=x²+a(a&gt;0)的圖形是由y=x²的圖形向上平移a個單位而得。&quot;"/>
<element type="text" label="文字1">
	<show object="true" label="false"/>
	<objColor r="0" g="0" b="204" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<font serif="false" size="6" style="1"/>
	<startPoint  x="-10.82" y="0.8200000000000004" z="1.0"/>
</element>
<expression label="文字2" exp="&quot;y=x²&quot;"/>
<element type="text" label="文字2">
	<show object="true" label="false"/>
	<objColor r="255" g="0" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<font serif="false" size="6" style="1"/>
	<startPoint  x="1.7" y="2.34" z="1.0"/>
</element>
<expression label="文字3" exp="&quot;y=x²+a&quot;"/>
<element type="text" label="文字3">
	<show object="true" label="false"/>
	<objColor r="204" g="0" b="204" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<font serif="false" size="6" style="1"/>
	<startPoint exp="(0, a + 1)"/>
</element>
<expression label="text1" exp="&quot;2012.6.2阿培製&quot;"/>
<element type="text" label="text1">
	<show object="true" label="false"/>
	<condition showObject="a &gt; 2"/>
	<objColor r="102" g="102" b="255" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<font serif="false" size="16" style="1"/>
	<startPoint  x="5.78" y="0.9999999999999996" z="1.0"/>
</element>
</construction>
</geogebra>