November 27, 2008, at 03:48 AM by LFS -
Changed line 10 from:
%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 -
Changed line 2 from:
>>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]]
Changed line 27 from:
%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 -
Changed line 14 from:
(:div style="margin-left:40px":)
to:
(:div2 style="margin-left:40px":)
Changed lines 17-20 from:
(: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.
to:
(:div2end:)
----
Changed lines 20-22 from:
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":)
>>-<<
Changed lines 24-25 from:
(:div12end :)
to:
>>s9<<
Click and drag the slider buttons to change the function.
%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 :)
>>&<<
Deleted line 31:
Deleted lines 32-33:
>>-<<
(:divend:)
March 17, 2008, at 02:33 AM by LFS -
Changed lines 17-18 from:
->%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.
Changed lines 22-24 from:
----
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 :)
Changed lines 26-30 from:
%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:

(:div1end :)
>>-<<
(:divend:)
----
>>&<<
%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 -
Changed lines 42-43 from:
* [[root]] of a function
to:
* [[quadratic formula]], [[root]] of a function, [[x-intercept]]
* [[y-intercept]]
March 13, 2008, at 03:52 PM by LFS -
Changed line 2 from:
>>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]]
Changed line 10 from:
%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%%.
Changed line 56 from:
[][[glossary/T| Attach:main/tri_purple_up_a.gif ]]&nbsp;[[glossary/T| Up one level]]
to:
[][[glossary/Q| Attach:main/tri_purple_up_a.gif ]]&nbsp;[[glossary/Q| Up one level]]
March 13, 2008, at 02:15 PM by LFS -
Changed line 28 from:
* 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]]).
Changed line 36 from:
{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}
to:
{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 -
>>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]]
>><<
[[<<]]

----
[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; {$\color{blue}{ a \ne 0}$}. %%
>>&<<
->%sol s9%(If {$a=0$}, then it is a [[linear function]].
(:divend:)
>>&<<
----
>>&<<
%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:
* [[root]] of a function
* [[polynom]] (polynomial function)
** [[linear function]]
>>&<<
----

>>id=box4<<
(:commentbox:)
>><<

[table width=100%]
[row]
[][[glossary/T| Attach:main/tri_purple_up_a.gif ]]&nbsp;[[glossary/T| Up one level]]
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