GlossaryT.QuadraticFunction History

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November 27, 2008, at 03:48 AM by LFS -
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%def b%Definition:%% A [[glossaryT/polynomial]] of first degree in one variable is called a %red b%quadratic function%% or %red%quadratic equation%%.
to:
%def b%Definition:%% A [[glossaryT/polynomial]] of second degree in one variable is called a %red b%quadratic function%% or %red%quadratic equation%%.
March 17, 2008, at 02:40 AM by LFS -
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>>nav_bar<<%reg%athcasts&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%exa%Examples&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%pra%Practice%%&nbsp;&nbsp;&nbsp;&nbsp;%mor%More&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%up%[[glossary/Q]]
to:
>>nav_bar<<%reg%Mathcasts&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%exa%Examples&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%pra%Practice%%&nbsp;&nbsp;&nbsp;&nbsp;%mor%More&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%up%[[glossary/Q]]
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%pra b%&nbsp;&nbsp;&nbsp;BTW: %pra%Don't be fooled.%% Changing %yel%c%% does %c11%not%% change the size of the quadratic - it only moves it up and down!
to:
%pra b%&nbsp;&nbsp;&nbsp;BTW: %pra%Don't be fooled.%% Changing %yel%c%% does %c11 red%not%% change the size of the quadratic. It only moves it up and down!
March 17, 2008, at 02:38 AM by LFS -
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(:div style="margin-left:40px":)
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(:div2 style="margin-left:40px":)
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(:showhide init=hide div=div1 lshow="+" lhide="-":) Interactivity %sol s9%(:showhide init=hide div=div12 lshow="+" lhide="-":) Directions for interactivity%%
(:div1 id=div1 :)
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Click and drag the slider buttons to change the function.
to:
(:div2end:)
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BTW: Don't be fooled. Changing %yel%c%% does %c12%not%% change the size of the quadratic - it only moves it up and down!
to:
(:showhide init=hide div=div1 lshow="+" lhide="-":) %exa b%Interactivity%% %sol s9%(:showhide init=hide div=div12 lshow="+" lhide="-":) Directions for interactivity%%
(:div1 id=div1 style="margin-left:20px":)
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(:div12end :)
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>>s9<<
Click and drag the slider buttons to change the function.
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%pra b%&nbsp;&nbsp;&nbsp;BTW: %pra%Don't be fooled.%% Changing %yel%c%% does %c11%not%% change the size of the quadratic - it only moves it up and down!
>><<
(:div12end :)
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(:divend:)
March 17, 2008, at 02:33 AM by LFS -
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->%sol s9%(If {$ a=0 $}, then it is a [[linear function]].
(:divend:)
to:
(:showhide init=hide div=div1 lshow="+" lhide="-":) Interactivity %sol s9%(:showhide init=hide div=div12 lshow="+" lhide="-":) Directions for interactivity%%
(:div1 id=div1 :)
>>-<<
Click and drag the slider buttons to change the function.
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----
to:
BTW: Don't be fooled. Changing %yel%c%% does %c12%not%% change the size of the quadratic - it only moves it up and down!
(:div12 id=div12 :)
(:div12end :)
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%exa b%Example:%% &nbsp;&nbsp;{$ f(x)=3x^2+2x-1 $}&nbsp;&nbsp; is a quadratic function &nbsp;&nbsp;{$ а=3 \quad b=2 \quad c=-1 $}&nbsp;&nbsp;&nbsp; ([[glossary/quadraticFunctionex1|%exa u%other examples]])
to:
(:applet code="geogebra.GeoGebraApplet" codebase="Java/GeoGebra/" archive="http://www.geogebra.org/webstart/geogebra.jar" width="800" height="350" filename="http://mathcasts.org/mtwiki/uploads/GlossaryT/quadratic_func.ggb" showResetIcon="true" showToolBar="false" showMenuBar="false":)

(:div1end :)
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(:divend:)
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----
>>&<<
%exa b%Example:%% &nbsp;&nbsp;{$ f(x)=3x^2+2x-1 $}&nbsp;&nbsp; is a quadratic function &nbsp;&nbsp;{$ а=3 \quad b=2 \quad c=-1 $}&nbsp;&nbsp;&nbsp; ([[glossary/quadraticFunctionex1|%exa u%other examples]])
>>&<<
March 14, 2008, at 04:46 AM by LFS -
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* [[quadratic formula]]
* [[root]] of a function
to:
* [[quadratic formula]], [[root]] of a function, [[x-intercept]]
* [[y-intercept]]
March 13, 2008, at 03:52 PM by LFS -
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>>nav_bar<<%reg%athcasts&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%exa%Examples&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%pra%Practice%%&nbsp;&nbsp;&nbsp;&nbsp;%mor%More&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%up%[[glossary/T]]
to:
>>nav_bar<<%reg%athcasts&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%exa%Examples&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%pra%Practice%%&nbsp;&nbsp;&nbsp;&nbsp;%mor%More&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%up%[[glossary/Q]]
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%def b%Definition:%% A %red b [[glossaryT/polynomial]] of first degree in one variable is called a %red b%quadratic function%% or %red%quadratic equation%%.
to:
%def b%Definition:%% A [[glossaryT/polynomial]] of first degree in one variable is called a %red b%quadratic function%% or %red%quadratic equation%%.
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[][[glossary/T| Attach:main/tri_purple_up_a.gif ]]&nbsp;[[glossary/T| Up one level]]
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[][[glossary/Q| Attach:main/tri_purple_up_a.gif ]]&nbsp;[[glossary/Q| Up one level]]
March 13, 2008, at 02:15 PM by LFS -
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* The intersection of the parabola with {$ y $}-axis is unique and is the point (0,с).
to:
* The intersection of the parabola with {$ y $}-axis is unique and is the point (0,с) (see [[y-intercept]]).
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{gg width=200; height=200; xmin=-5; xmax=5; xscl=1; ymin=-8; ymax=3; yscl=1; axes(); stroke="#009900"; strokewidth=3; plot("x^2-x-6"); strokewidth=2; stroke="#660000"; dot([-2,0],"closed"); a=text([-2,0],"корен",aboveleft); dot([3,0],"closed"); b=text([3,0],"корен",aboveright); stroke="#660099"; dot([0,-6],"open"); c=text([0,-6],"y-пресек",belowleft) gg}
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{gg width=200; height=200; xmin=-5; xmax=5; xscl=1; ymin=-8; ymax=3; yscl=1; axes(); stroke="#009900"; strokewidth=3; plot("x^2-x-6"); strokewidth=2; stroke="#660000"; dot([-2,0],"closed"); a=text([-2,0],"root",aboveleft); dot([3,0],"closed"); b=text([3,0],"root",aboveright); stroke="#660099"; dot([0,-6],"open"); c=text([0,-6],"y-intercept",belowleft) gg}
March 13, 2008, at 02:12 PM by LFS -
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(:title Quadratic Function:)
>>nav_bar<<%reg%athcasts&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%exa%Examples&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%pra%Practice%%&nbsp;&nbsp;&nbsp;&nbsp;%mor%More&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;%up%[[glossary/T]]
>><<
[[<<]]

----
[table border=1 cellpadding=5 width=98%]
[row]
[]>>&<<
%def b%Definition:%% A %red b [[glossaryT/polynomial]] of first degree in one variable is called a %red b%quadratic function%% or %red%quadratic equation%%.
>>&<<
The general form of a quadratic function is:
>>&<<
(:div style="margin-left:40px":)
{$ \color{red}{ f(x)=ax^2+bx+c} $} &nbsp;&nbsp; или &nbsp;&nbsp; {$ \color{red}{y=ax^2+bx+c} $}&nbsp;&nbsp; where &nbsp;&nbsp; {$\color{blue}{ a \ne 0} $}. %%
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->%sol s9%(If {$ a=0 $}, then it is a [[linear function]].
(:divend:)
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----
>>&<<
%exa b%Example:%% &nbsp;&nbsp;{$ f(x)=3x^2+2x-1 $}&nbsp;&nbsp; is a quadratic function &nbsp;&nbsp;{$ а=3 \quad b=2 \quad c=-1 $}&nbsp;&nbsp;&nbsp; ([[glossary/quadraticFunctionex1|%exa u%other examples]])
>>&<<
[table]
[]%reg b%Rules:%%
&nbsp;
* The%pra% graph%% of every quadratic function a %ans%parabola%%.
* The intersection of the parabola with {$ y $}-axis is unique and is the point (0,с).
* The intersections of the parabola with {$ x $}-axis (if there is any), are the roots of the function and can be found with the [[quadratic formula]].

(:div align=right:)
The graph shown at right is of the quadratic function:
%pra s12%{$ y=x^2-x-6 $}%%&nbsp;&nbsp; -->
(:divend:)
[c width=230]
{gg width=200; height=200; xmin=-5; xmax=5; xscl=1; ymin=-8; ymax=3; yscl=1; axes(); stroke="#009900"; strokewidth=3; plot("x^2-x-6"); strokewidth=2; stroke="#660000"; dot([-2,0],"closed"); a=text([-2,0],"корен",aboveleft); dot([3,0],"closed"); b=text([3,0],"корен",aboveright); stroke="#660099"; dot([0,-6],"open"); c=text([0,-6],"y-пресек",belowleft) gg}
[tableend]
>>&<<
-------------
>>&<<
%rel%Related topics:
* [[quadratic formula]]
* [[root]] of a function
* [[polynom]] (polynomial function)
** [[linear function]]
>>&<<
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[][[glossary/T| Attach:main/tri_purple_up_a.gif ]]&nbsp;[[glossary/T| Up one level]]
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Page last modified on November 27, 2008, at 03:48 AM