Lesson 2 You-Mix Cubes Solidify Understanding
Identify the key features of
Graph each of the following functions using transformations of
Compare quadratic and cubic functions.
Graph cubic functions.
What are the similarities and differences between quadratic functions and cubic functions?
Open Up the Math: Launch, Explore, Discuss
Previously, we learned that the function generated by the sum of the terms in a quadratic sequence is called a cubic function. Linear functions, quadratic functions, and cubic functions are polynomials, which also include functions of higher powers. In this lesson, we will explore more about cubic functions to learn some of the similarities and differences between cubic functions and quadratic functions.
To begin, let’s take a look at the most basic cubic function,
Use a table to verify that
Describe the features of
Using your knowledge of transformations, graph each of the following without using technology.
Use technology to check your graphs above. What transformations did you get right? What areas do you need to improve on so that your cubic graphs are perfect?
Since quadratic functions and cubic functions are both in the polynomial family of functions, we would expect them to share some common characteristics. List all the similarities between
As you can see from the graph of
The range of
Ready for More?
What similarities do you expect to exist between
*The similarities between
In this lesson, we examined the features of the cubic parent function,
Use the graph to write the equation of the quadratic function in factored form.
How can you use the equation to find the
Write an equivalent expression: