## Why do we graph Polynomial Functions?

Basically, the graph of a polynomial function is a smooth continuous curve. There are several main aspects of this type of graph that you can use to help put the curve together. We will also be looking at finding the zeros, aka the x-intercepts, as well as the y-intercept of the graph.

**What are examples of polynomial graphs?**

Here are some examples of polynomial functions and the language we use to describe them:

f(x)=3x−2 | Linear polynomial (linear function) |
---|---|

f(x)=x2−4x+1 | Quadratic polynomial |

f(x)=−3×3+x−6 | Cubic polynomial with no quadratic term |

f(x)=(x−3)2(2x−1) | Cubic polynomial (convince yourself that the largest power will be three when expanded) |

### What are the characteristics of the graph of a polynomial function?

Recognizing Characteristics of Graphs of Polynomial Functions. Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous.

**What are the important concepts in understanding and describing polynomial functions?**

A polynomial function consists of either zero or the sum of a finite number of non-zero terms, each of which is a product of a number, called the coefficient of the term, and a variable raised to a non-negative integer power.

#### How can you apply polynomial functions in solving real life problems?

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.

**How are polynomials used in physics?**

Polynomials are even used in various fields of science , such as physics , where we measure acceleration , or to express units of energy , inertia , or even in electricity . etc . In chemistry , polynomials are used in writing down the chemical equations .

## How do you graph polynomial functions?

To graph polynomial functions, find the zeros and their multiplicities, determine the end behavior, and ensure that the final graph has at most turning points. See (Figure) and (Figure). Graphing a polynomial function helps to estimate local and global extremas. See (Figure).

**What is the graph of a polynomial function with odd multiplicities?**

The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is no greater than the degree of the polynomial function.

### Which polynomial function has at most turning points?

A polynomial function of degree has at most turning points. See (Figure). To graph polynomial functions, find the zeros and their multiplicities, determine the end behavior, and ensure that the final graph has at most turning points. See (Figure) and (Figure).

**Are all graphs of polynomial functions smooth and continuous?**

Figure 2. The graphs of and are graphs of polynomial functions. They are smooth and continuous. The graphs of and are graphs of functions that are not polynomials. The graph of function has a sharp corner. The graph of function is not continuous. Do all polynomial functions have as their domain all real numbers? Yes.