• East Asian mathematical journal
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• v.37 no.2
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• pp.265-288
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• 2021

In the 2015 revised mathematics curriculum, the system of equations is first introduced in 'Variables and Expressions' of [Middle School Grades 1-3]. Then, It is constructed that after learning the linear function in 'Functions', the relationship between the graphs of two linear functions and the systems of linear equations are learned so that students could improve the geometric representation of the systems of equations. However, in of Elective-Centered Curriculum Common Courses, Instruction is limited to algebraic manipulation when teaching and learning systems of quadratic equations. This paper presented the teaching and learning method that can improve students' mathematical connection through various representations by providing geometric representations in parallel using GeoGebra, a mathematics learning software, with algebraic solutions in the teaching and learning situation of simultaneous quadratic equations.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.819-825
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• 2016

In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.275-284
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• 2005

In the present paper we shall introduce several operators on the reproducing kernel spaces. And using them we shall find a solution of an infinite system of quadratic equations (1.1). In particular we shall convert problem for finding an approximate solution of infinite system of quadratic equations into problem for minimizing nonnegative biquadratic polynomial.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.31-37
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a functional equation and a system of functional equations on Jensen-quadratic mappings.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.411-424
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• 2010

In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.545-567
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• 2023

This study investigates effective ChatGPT prompts for solving mathematical problems, focusing on the chapters of quadratic equations and quadratic functions. A structured prompt was designed, following a sequence of 'Role-Rule-Example Solution-Problem-Process'. In this study, an artificial intelligence model combining GPT-4, Wolfram plugin, and Advanced Data Analysis was utilized. Wolfram was used as the primary tool for calculations to reduce computational errors. When using the structured prompt, the accuracy rate for problems from nine high school mathematics textbooks on quadratic equations and quadratic functions was 91%, showing higher performance compared to zero-shot prompts. This confirmed the effectiveness of the structured prompts in solving mathematical problems. The structured prompts designed in this study can contribute to the development of intelligent information systems for personalized and customized education.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.123-132
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• 2014

In this paper, we investigate the following form of a certain class of quadratic functional equations and its fuzzy stability. $$f(kx+y)+f(kx-y)=f(x+y)+f(x-y)-2(1-k^2)f(x)$$ where k is a fixed rational number with $k{\neq}1$, -1, 0.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.321-330
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• 2015

In this paper, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x - y) = f(x + y) + f(x - y) + 4f(x) + 2f(-x) in modular spaces by using a fixed point theorem for modular spaces.