# Lesson 1 Transformers: Shifty y’s Develop Understanding

## Learning Focus

Find patterns in the equations and graphs of quadratic functions.

What happens to the graph of

## Open Up the Math: Launch, Explore, Discuss

Optima Prime is designing a robot quilt for her new grandson. She plans for the robot to have a square face. The amount of fabric that she needs for the face will depend on the area of the face, so Optima decides to model the area of the robot’s face mathematically. She knows that the area

### 1.

What is the domain of the function

### 2.

Match each statement about the area to the function that models it.

___

The length of each side is increased by

units. ___

The length of each side is multiplied by

units. ___

The area of a square is increased by

square units. ___

The area of a square is multiplied by

.

### 3.

Optima started thinking about the graph of

Optima began wondering about how changes to the equation of the function, like adding

### 4.

Make your own predictions of how the graphs of each of the following equations will be the same or different from the graph of

Similarities to the graph of | Differences from the graph of | |
---|---|---|

### 5.

Optima decided to test her ideas using technology. She thinks that it is always a good idea to start simple, so she decides to go with

### 6.

Knowing that things make a lot more sense with more representations, Optima tries a few more examples, like

### 7.

After her amazing success with addition in the last problem, Optima decided to look at what happens with addition and subtraction inside the parentheses, or as she says it, “Adding to the

### 8.

Optima thought that problem 7 was very tricky and had hoped that multiplication was going to be more straightforward. She decides to start simple and multiply by

### 9.

Optima is encouraged because she was able to figure out the last problem. She decides to end her investigation for the day by determining the effect of a multiplier,

## Ready for More?

Use technology to explore the behavior of the line

## Takeaways

Equation | Transformation of |
---|---|

## Adding Notation, Vocabulary, and Conventions

Vertex:

Line of Symmetry:

## Lesson Summary

In this lesson, we explored transformations of the function

Draw a line of symmetry for the graph, state whether the graph has a maximum point or a minimum point, and provide the coordinates for that point.

### 1.

### 2.

Graph the linear equations, and explain your strategy.