Investigating Parabolas

The first 200 words of this essay...

Description

In this task, you will investigate the patterns in the intersections of parabolas and the lines y = x and y = 2x. Then you will be asked to prove your conjectures and to broaden the scope of the investigation to include other lines and other types of polynomials.

Background

Functions: 1)=ax + b, a = 0 - Linear Equation

2) ax2+ bx+c - Quadratic

3) ax3+ bx2+cx+d - Cubic

4) ax4+ bx3+cx2+dx+e - Quartic

Introduction

The investigation of parabola brings me to think and promote my knowledge about quadratic functions. Also, it helps me to find the 'patterns' and 'rules' of parabola which was another great source to improve my mathematic skills. In the HL type I, it asks about thoughtful questions such as relationship between parabolas and lines. There are six questions in this portfolio and each question requires rumination. I will try to focus on the member of the family of polynomials precisely since they are the basic functions of these problems and it will help me to 'link' some ideas. Equally important, interestingly, this portfolio wants the student to find their 'own' conjecture. Thus,