# Lesson 5 Transformers: More Than Meets the y’s Solidify Understanding

## Jump Start

Without using technology, match each of the equations with the graph of the function. Be careful; there are more graphs than equations!

___

___

___

___

## Learning Focus

Write equations for functions that are transformations of

Find efficient methods for graphing transformations of

What happens to the graph of

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

In the previous lesson, you learned about transformations of the graph of

### 1.

Identify each anchor point shown on the graph of

Anchor points:

Vertex

and and and

Line of symmetry:

Write the equation for each problem below. Use a second representation to check your equation.

### 2.

The area of a square with side length

### 3.

### 4.

### 5.

Graph each equation without using technology. Be sure to have the exact vertex and at least two correct points on either side of the line of symmetry.

### 6.

### 7.

### 8.

### 9.

Given:

#### a.

What point is the vertex of the parabola?

#### b.

What is the equation of the line of symmetry?

#### c.

How can you tell if the parabola opens up or down?

#### d.

How do you identify the vertical stretch?

### 10.

Does it matter in which order the transformations are done? Explain why or why not.

## Ready for More?

Think about applying the transformations to the parent function

### 1.

What point makes sense to use as an anchor point on this function?

### 2.

What do you think is the equation of the function with a horizontal shift left

### 3.

How does the horizontal shift on

## Takeaways

Vertex form of a quadratic equation:

Vertex:

Line of symmetry:

Vertical stretch:

Opens upward:

Opens downward:

Quick-graph method for graphing quadratics:

a.

c.

b.

## Vocabulary

- vertex form
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we learned to graph quadratic functions that have a combination of transformations. We found that the vertex form of the equation of a quadratic function makes it easy to find the vertex and identify the transformations. We wrote equations in vertex form from graphs and tables, using our understanding of transformations and the features of parabolas.

The standard form for a quadratic equation is

### 1.

### 2.

### 3.

### 4.

### 5.

Use the table to identify the vertex, the equation for the line of symmetry, and state the number of

Vertex:

Line of symmetry:

-int(s): Minimum or maximum?