Leading coefficient test, Algebra

Assume that P ( x ) is a polynomial  along with degree n.  Thus we know that the polynomial have to look like,

                                                    P ( x ) =axn..............

We don't know if there are any other terms in the polynomial; however we know that the first term will need to be the one listed as it has degree n. Now we have the following facts regarding the graph of P ( x ) at the ends of the graph.

1.   If a> 0 and the value of n is even then the graph of P ( x )will increase without restricts positively at both endpoints.  A good instance of this is the graph of x2.

2369_Leading Coefficient Test.png

2.   If a= 0 and the value of n is odd then the graph of P ( x ) will increase without bound positively at the right end and decrease without bound at the left end.  A good instance of this is the graph of x3.

1749_Leading Coefficient Test1.png

3.   If a= 0 and the value of n is even then the graph of P (x ) will decrease without  any bound positively at both of the endpoints.  A good instance of this is the graph of -x2.

900_Leading Coefficient Test2.png

4.   If a= 0 and the value of n is odd then the graph of P ( x ) will decrease without  any bound positively at the right end and increase without  any bound at the left end.  A good instance of this is the graph of -x3.

990_Leading Coefficient Test3.png

Okay, now that we've obtained all that out of the way finally we can give a procedure for getting a rough sketch of the graph of a polynomial.

Posted Date: 4/8/2013 2:48:10 AM | Location : United States







Related Discussions:- Leading coefficient test, Assignment Help, Ask Question on Leading coefficient test, Get Answer, Expert's Help, Leading coefficient test Discussions

Write discussion on Leading coefficient test
Your posts are moderated
Related Questions

what is quarditic equation

First method draws back                          Consider the following equation.                                                                7 x   = 9 It is a fairly

10 to the 50th exponent

The point where the two asymptotes cross is known as the center of the hyperbola. Standard forms There are two standard forms of the hyperbola, one for each type illustrate

Finance is the field of science that explains the management of funds. The areas that generally come under finance are personal finance, business finance, and public finance. The f

Miscellaneous Functions The importance of this section is to introduce you with some other functions that don't really need the work to graph that the ones which we've looked

Do you accept screen shot because it is a graph.


I am trying to find the answer to y=x^2+12x-11 Would you help me