Quadratic Polynomials. Real and Imaginary components

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MATHS IA                                                                                                             Alex Chen

PART A (Quadratic Polynomials)

The investigation is to find out if the zeros and to determine the real and imaginary components of the complex zeros of


From the function given,

The coordinates of the vertex is

by using  the Quadratic equation:



has zeros

, and

By subbing in different numbers of

into the equation:


, it is given that

, which is equal to







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After subbing different values for


From the above results,

by comparing with

, it can be seen that their values are opposite,

 have negative results,  

’s results are always a positive number or bigger than 0.

A graph of y1 and y2 is shown below when a= 3 and b=5,

We know that

has zeros

, while

 has opposite concavity to

,which is in the form


From the graph, it can be seen that,

is a reflection of


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