Parametric' Investigation and Classification of Quadratic Equation

Abstract- This study investigated the parameters space of simple and familiar quadratic equation often encounter in science based disciplines and in particular engineering. The aim is strange images creation to excite and launch novices to quest for general understanding of fractal taking parallel clue from Julia and Mandelbrot sets creation using the iterative mechanism of complex quadratic mapping. Preliminary computation of a Julia and Mandelbrot sets was performed on a square complex plane using coarse step size .Using normalization technique, the three parameters space of a general quadratic equation was reduced to two parameters space. Thereafter, several parameters combination drawn from within the range of two square 'parameters window specification was tested according to root values outcome using the popular 'Almighty formula'. The root values outcomes were classified into three distinct groups: complex roots, equal real roots and different real roots. Curve fitting ratio and graphical analyses were performed on each group based on content and as applicable. The preliminary results of a Julia and Mandelbrot sets are acceptable to within the tolerance of coarse step size. The reduced two dimension parameters space was partioned by parabolic curve into two sub-blocks in favour of complex roots and different real roots outcomes. The sub-block in favour of different real roots dominate consistently over studied cases. The ratios of different real roots to complex roots gravitate respectively to 5.71 and 1.40 for longer and smaller windows with decreasing step size. The graphical analyses reveal strange fractal like images for cases investigated. The founding's of this study can be utilized to gently and safely launch both High School and College students to the world of fractal science, as the images generated are exciting and amazing..