Ib math HL portfolio parabola investigation

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Math HL Portfolio

Parabola Investigation

INTRODUCTION

In this portfolio I am going to investigate the patterns formed when a parabola,

y=ax2+bx+c intersects with the lines y=x and y=2x. Further I would be broadening the scope of this investigation to other lines and other orders of polynomials and observing patterns in their respective intersections.

The first part of my portfolio would include parabolas with their turning points located in the 1st quadrant of a graph. I would be investigating the patterns formed when the two lines y=x and y=2x intersect with parabolas that have different coefficients of x2 but lie in the first quadrant and form a conjecture. Then I would prove it and test its limitations.

The second part would include testing and modifying my conjecture for the turning point of the parabola situated in any quadrant and testing for all real co-efficient of x2.

The third part would include modifications to the conjecture if the intersecting lines are changed and hence finding its limitations.

In the final part of my portfolio I will also try and make a conjecture for polynomials of higher order and derive any