All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

In a function such as sine or cosine, we could also have a translation of the form: \(y = \sin (x - a)^\circ\) where \(a\) is called the phase angle. This is when the graph of the function has been ...

Mathematical methods and special functions have long served as the backbone of modern theoretical physics and applied mathematics. These tools enable researchers to solve complex differential ...

(1) MR. Pressland adopts the heuristic method in this course of experimental geometry for beginners. The first exercises only require the use of a pencil and a graduated straight edge cut from ruled ...