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Algebra> Linear transformations of the parabola and the hyperbola 
Visual didactic materials
Slidefilms of the series «Linear transformations of the parabola and the hyperbola» These films can be reproduced on any computer having WINDOWS version 95 (and higher versions) without an additional installation of special programmes as they are made in EXE format. The principle of operation: the changing of frames is executed by pushing of a printed(graphical) button. Movement is is possible both “forward” and “backward”. Slidefilms are meant for group study and can be used by a teacher at school lessons spontaneity.The principle of operation the film offering by us gives an opportunity to stop at the frames demanding special attention. 
¹1. The directional rectangles of the parabola  

The film shows how to construct the parabola
rather exactly on plotted paper without a curve –the graph of functiony=x^{2}.
It’s useful to pay attention of students to comfortable for construction the big and small
directional rectangles, which visually substitute the habitual table of significations of the square dependence
y=x^{2}in points õ= 2;1;0;1;2.  
¹2. The directional rectangles of the hyperbola  

The film shows how to construct the hyperbola
rather exactly on plotted paper without a curve – the graph of function y=1/x.
It’s useful to pay attention of students to comfortable for construction squares,
vertical and horisontal rectangles which visually substitute the habitual significations table of the
inverse dependence y=1/x in points õ= 2;1;0;1;2.  
¹3. The shifts of the directional rectangles of the parabola along the axis of ordinate  
The film shows how to make shifts of the parabola easily
along the axis of ordinate on the base of already known ways
The connecnion between the sign of numerical parameterÂ
in setting the function y=x^{2}±Â and the distance
in which the graph of function y=x^{2} shifts with its directional rectangles
should be paid attention of students to. 

¹4. The shifts of the directional rectangles of the hyperbola along the axis of ordinate  

The film shows how to make shifts of the hyperbola easily
along the axis of ordinate on the base of already known ways.
The connecnion between the sign of numerical parameterÂ
in setting the function y=1/x±Âand the distance
in which the graph of function y=1/x shifts with its directional
rectangles should be paid attention of students to.


¹5. The deformation of the directional rectangles of the parabola along the axis of ordinate  

The film shows how to make the deformation of the parabola easily
along the axis of ordinate with the help of compressing and stretching of the directional rectangles.
The connecnion between the sign of numerical parameter À
in setting the function y=À^{.}x^{2}
and stretching or compressing the graph of starting function y=x^{2}
takes with its directional
rectangles depending on the significance of the parameter should be paid attention of students to.
 
¹6. The deformation of the directional rectangles of the hyperbola along the axis of ordinate  

The film shows how to make the deformation of the hyperbola easily
along the axis of ordinate with the help of compressing and stretching of the directional rectangles.
The connecnion between the sign of numerical parameter À
in setting the function y=À/x
and stretching or compressing the graph of starting function y=1/x
takes with its directional
rectangles depending on the significance of the parameter should be paid attention of students to.
 
¹7. The shifts of the directional rectangles of the parabola along the axis of abscissa  

The film shows how to form the algorithm of shifting of the parabola with its directional rectangles
along the axis of abscissa on the base of already known ways.
The connecnion between the sign of numerical parameter ð
in setting the function y=(x±ð)^{2}
and the distance
in which the graph of function y=x^{2}
moves with its directional
rectangles should be paid attention of students to.


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Algebra> Linear transformations of the parabola and the hyperbola 
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