Keyword: «parabola»

To increase the level of mathematical preparation of schoolchildren and university entrants choosing technical and mathematical specialties of universities in school geometry lessons and in the process of preparing for the passing of the USE in mathematics (profile level), special attention should be given to those mathematical questions, without profound knowledge of which successful learning in higher educational institution would be impossible. In this article we give examples of solving problems with parameters. They are offered as increased difficulty problems when passing the USE. One of the differentiated approach possibilities of future students’ preparation is demonstrated who will have to learn the analytical geometry course among other courses. The examined problems show the advantages of graphical solution application with the help of second-order curves. The content of the article may be interesting to teachers, high school students, who are preparing to enter higher educational institutions for technical and mathematical specialties.

The relevance of this work relates to the special place of the lines and surfaces of the second order in the courses of analytical geometry and engineering graphics at the technical University. Parabola and corresponding to it in three-dimensional world paraboloid, play an important role in many physical processes. As a result, they have found wide application in many engineering, technical and other devices, architecture, and just in everyday life. In this article, the authors examine the mathematical properties of parabola and paraboloid and the peculiarities of their graphical representation. The content of the article will be interesting for students of engineering and mathematics, teachers of mathematics and engineering graphics, as well as for high school students preparing to enter universities to study technical or mathematical sciences, since prospects of modern school education development are associated with the growing role of its polytechnic component.