A polynomial function is an expression of restricted span make since variables and constants. Polynomials functions are using as single provides of adding, subtraction, multiplication, and entire-number exponent. Polynomials function present in a broad variety of area of math and science. Sketching polynomial is a method of simplifying the given polynomial function and make a graph for this solution. This article give number of examples of sketching polynomial function. Let, us see the examples of sketching polynomial functions

Examples of Sketching Polynomial Functions:

Example 1:

Sketching the graph for the given polynomial function:

Y=5x^{3}-10x^{2}-20x+40

**Solution:**

Given polynomial function is Y=5x^{3}-10x^{2}-20x+40

Let we can write this as:

5x^{2}(x-2)-20(x-2)

Take the common factor that is (x-2)

= (x-2)(5x^{2}-20)

= (x-2)(5)(x^{2}-4)

= (x-2)(5)(x-2)(x+2)

= 5(x+2)(x-2)^{2}=0 (where x=-2 and x=2)

Now mark the point on the graph which is shown in the below figure:

By (x-2)^{2} again the graph can be draw as:

Which is the required sketching graph for the given function Y=5x^{3}-10x^{2}-20x+40.

**Example 2:**

Sketching the graph for the given polynomial function:

Y=(x-1)(x+3)^{2}

**Solution:**

Given function is y=(x-1)(x+3)^{2}

Let, take the value of x=1 and x=-3 then the function is simplified as:

0=(x-1)(x+3)^{2}

Now the graph we obtain as:

By the value of (x+3)^{2} the final graph we get as:

Which is the required sketching graph for the given function Y=(x-1)(x+3)^{2}.

One more Example of Sketching Polynomial Function:

Consider the polynomial P(x) with degree n. hence, we know that the polynomial is like that.

P(x)=cx^{n}+…..

**Example 3:**

In P(x)=cx^{n}+…., if the c>0 and n is even then the sketching of graph for P(x) will grow without bound positively at both end peaks. A perfect example of the function
x^{2} is given below.

**Example 4:**

Draw a graph for the polynomial function P(x)=x^{3}.

**Solution:**

Given P(x)=x^{3}.

The graph for the given polynomial is defined below.