Visual didactic materials
«Linear transformations of the parabola and the hyperbola»

           Slide-films of the series «Linear transformations of the parabola and the hyperbola»
are meant to form elementary ideas of the graphs of the elementary functions.

           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”.

           Slide-films 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.

Linear transformations of the parabola and the hyperbola

       The film shows how to construct the parabola rather exactly on plotted paper without a curve –the graph of functiony=x².

       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=x²in points х= -2;-1;0;1;2.

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       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 х= -2;-1;0;1;2.

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       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 parameterВ in setting the function y=x²±В and the distance in which the graph of function y=x² shifts with its directional rectangles should be paid attention of students to.

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       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 parameterВ in setting the function y=1/x±Вand the distance in which the graph of function y=1/x shifts with its directional rectangles should be paid attention of students to.

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       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 А in setting the function y=А^.x² and stretching or compressing the graph of starting function y=x² takes with its directional rectangles depending on the significance of the parameter should be paid attention of students to.

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       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 А in setting the function y=А/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.

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       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 р in setting the function y=(x±р)² and the distance in which the graph of function y=x² moves with its directional rectangles should be paid attention of students to.

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Conception and visualisation - Reznik N.A.

Planning and visual organisation - Yezhova N.M.

Testing and approving - Karasev A.A.

Mathematical editing and тesting - Temnikova I.S.

© Natalya Reznik (nareznik@yandex.ru): the chief of the project “The visual school”
© Natalia Yezhova (naegova@yandex.ru): the methodologist-elaborator of the web site
© Aleksey Baryshkin: design the mock-up of the web site
© Anrey Karasev: translator