Question

How are the zeros of a polynomial function used to create a graph

Answer 1

General Rule

If the Polynomial is of degree n, then it has n zeroes, then it cuts x axis at n points.

Now, explaining the above rule

→If a polynomial has single zero, then it cuts x axis at one point, which will be linear function ,like , x=a.

→If the polynomial cuts x axis at two points, it means it has two zeroes ,which will be a quadratic function.

→Like wise, Polynomial of third degree cuts x axis at three points and it will be a cubic polynomial.

How Zeros of a polynomial function used to create a graph

⇒Now, suppose the two zeroes of function are ,a and b.

 x=a and x=b.That is, x-a=0 and x-b=0

To Obtain the function, multiply the two linear function

 (x-a)(x-b)=0

Which gives a Quadratic function.

→x² -(a+b)x+ab=0

⇒Similarly, for three roots (a,b,c) of the function,the function will be

 →x³-(a+b+c)x²+(ab+bc+ca)x²-abcx+k(Constant)=0

Which will be a Cubic function.

Answer 2

11 . Predict the end behavior of the function.

22 . Find the real zeros of the function. Check whether it is possible to rewrite the function in factored form to find the zeros. Otherwise, use Descartes' rule of signs to identify the possible number of real zeros.

33 . Make a table of values to find several points.

44 . Plot the points and draw a smooth continuous curve to connect the points.

55 . Make sure that the graph follows the end behavior as found in the above step.