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Polynomial Graphs

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More Lessons for Intermediate Algebra or Algebra II lessons

Math Worksheets

A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

  • how to graph polynomials
  • how to transform polynomial graphs

Basic Polynomial Graphs

Graphing higher degree polynomial functions can be more complicated than graphing linear and quadratic functions. Polynomial graphs can be graphs of functions where the degree of the highest term is greater than one. When we graph polynomials with varying degrees it is easier to identify the end behavior, shape and turning points.

Review Graphs of Quadratics
Exploring Quadratic Graphs
Graphing Quadratic Equations

This video provides and example of how to graph a cubic or degree 3 polynomial function by completing a table of values.

Graphing cubic functions with the help of a calculator

How we identify the end behavior of a polynomial functions.
Here we learn to sketch the curve of a polynomial function without the aid of a graphing calculator. Also, no calculus methods will be used.

This video shows how to graph y = -5x4 -30x3 - 45x2 and we learn about "bouncing" x intercepts.

Basic Transformations

When graphing polynomials, basic transformations occur when a graph either shifts along the x-axis or y-axis and/or dilates. When graphing transformations, a dilation occurs when the "a" term value is changed. Dilations cause the parabola to either open a different direction or change shape. A shift occurs when a graph doesn't change shape but moves along the x or y axis.

Review Transformation of Quadratic Graphs
Vertical and Horizontal Shifts of Quadratic Graphs
Dilations of Quadratic Graphs

How to graph a Transformation of a Cubic Function

Transformation of polynomial functions
A quick lesson on transformations with polynomial functions.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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