The information presented here is intended to describe the course goals for current and prospective students as well as others who are interested in our courses. It is not intended to replace the ...

For a quadratic equation of the form \(y = k{(x - a)^2} + b\), the following diagram shows the main properties: If k > 0, the vertex is a minimum turning point If k < 0, the vertex is a maximum ...

In this example, both the numerator and the denominator can be factorised. The numerator is a quadratic with no common factors which will therefore factorise into two brackets. The denominator ...

rational, and power function. Additional topics with functions included such as transformations of graphs and symmetry, composite functions, one-to-one and inverse functions. Solving linear and ...

Algebraic dynamics and differential equations are fields that explore ... for Lax representations and the existence of quadratic rational first integrals, which are essential for understanding ...

and number theory to uncover deeper insights into the dynamics of rational maps. One significant area of recent research is the study of preperiodic points for quadratic polynomials. A preperiodic ...