Transformations of Quadratic Functions

Section 2.1 beginning on page 48.

The Big IdeasIn this section we will learn about….

• Describing transformations of quadratic functions (extension of section 1.2)

o Translations (horizontal and vertical)o Reflections (in the x-axis and the y-axis)o Stretches and Shrinks (horizontal and vertical)

• Writing transformations of quadratic functions.

o NEW: Writing transformed quadratic functions in vertex form. o Writing transformed quadratic functions, applying transformations one at

a time. (extension of section 1.2)

Core Vocabulary

Previously Learned:

• Transformations

New Vocabulary:

• Quadratic Function• Parabola• Vertex of a Parabola• Vertex Form

Quadratic FunctionsA quadratic function is a function that can be written in the form where .

The U-shaped graph of a quadratic function is called a parabola.

In the previous chapter we graphed quadratic functions using tables of values. In this section we will learn to graph quadratic functions using the transformations to the parent function .

(Why can’t a=0 ? )

Translations

Describe each transformation:

1) 2) 3) 4)

Translation 4 units left

Translation 3 units right

Translation 1 unit up Translation 2 units down

Translations

Reflections

Stretches and Shrinks

Transformations of Quadratic Functions

Vertex Form** This is new and important, put this in your notes **

Writing a Transformed Quadratic Function

This is a new technique

This is a previously learned technique

New: Method 1

Writing a Transformed Quadratic Function

Lets work this step out

Practice

(From example 5: )