# Lesson 2 You-Mix Cubes Solidify Understanding

## Jump Start

### 1.

Identify the key features of

### 2.

Graph each of the following functions using transformations of

#### a.

#### b.

#### c.

## Learning Focus

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, **degree **** polynomial** because the highest exponent is **degree **** polynomials** but are called quadratic after the Latin word for *square*. Scott’s March Motivation showed that linear functions have a constant rate of change, quadratic functions have a linear rate of change, and cubic functions have a quadratic rate of change.

### 1.

Use a table to verify that

### 2.

Graph

### 3.

Describe the features of

### 4.

Using your knowledge of transformations, graph each of the following without using technology.

#### a.

#### b.

#### c.

#### d.

### 5.

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?

### 6.

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

### 7.

As you can see from the graph of **why** each statement is true by completing the sentence.

#### a.

The range of

#### b.

For

#### c.

For

## Ready for More?

What similarities do you expect to exist between

## Takeaways

*Similarities between | Differences in |
---|---|

*The similarities between

## Vocabulary

- cubic function
- degree of a polynomial
- polynomial function
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we examined the features of the cubic parent function,

### 1.

#### a.

Use the graph to write the equation of the quadratic function in factored form.

#### b.

How can you use the equation to find the

### 2.

Write an equivalent expression: