An approach towards intuitively understanding the vertex and axis of symmetry of a parabola without completing the square is presented. The main aims of this study are to help learners comprehend the following two problems: (1) the reason why the position of an axis of symmetry is essentially determined only by the coefficient of a first-order term, and (2) the reason why the positive and negative of the coefficient of the first-order term are opposite to the positive and negative of the horizontal coordinates of the axis of symmetry. The method of graphing parabolic motion is also presented as a cross-study with kinematics.

parabola, quadratic function, vertex, axis of symmetry.

Received: August 16, 2024; Accepted: September 13, 2024; Published: October 15, 2024

How to cite this article: Yukio Kobayashi, Intuitive understanding of the vertex and axis of symmetry of a parabola without completing the square, Far East Journal of Mathematical Education 26(2) (2024), 99-108. http://dx.doi.org/10.17654/0973563124010

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Nivaldo A. Lemos, On the least uncomfortable journey from A to B, Eur. J. Phys. 40 (2019), 055802.
[2] F. M. de la Rosa, Comparing the widening of two parabolas, Far East Journal of Mathematical Education 20(3) (2020), 95.
[3] International Union of Pure and Applied Chemistry, Quantities, Units and Symbols in Physical Chemistry, IUPAC, 2007.
[4] Yukio Kobayashi, Derivation of some formulae in combinatrics by heuristic method, International Journal of Mathematical Education in Science and Technology 46 (2015), 469-476. Erratum 46 (2015), 795.
[5] Yukio Kobayashi, Supplementary remarks on simple sum using dimensions – from viewpoint of connection to physics based on weighted average, Far East Journal of Mathematical Education 26(1) (2024), 55-70.