Translations of Quadratic Functions

​Algebra 1 Quadratics: Transformations Lesson:

Vertical and Horizontal Translations

​Overview: In this lesson you will learn how to describe and write transformations of quadratic functions.

​Quadratic Translation Rules:

​Quadratic Vertical Translation Rule: UP

​Quadratic Vertical Translation Rule: DOWN

​Quadratic Horizontal Translation Rule: RIGHT

​Quadratic Horizontal Translation Rule: LEFT

​Quick Review:

​​Test your skills over the next few questions.

​Translates f(x) 7 units up

​Translates f(x) 7 units down

​Translates f(x) 7 units right

​Translates f(x) 7 units left

Multiple Choice

If  $$f\left(x\right)=x^2$$  , which function would translate it 5 units left?

• $$f\left(x\right)=\left(x+5\right)^2$$  

• $$f\left(x\right)=x^2+5$$  

• $$f\left(x\right)=5x^2$$  

• $$f\left(x\right)=\left(x-5\right)^2$$  

Multiple Choice

If the blue is  $$f\left(x\right)=x^2$$  then the red must be

• $$g\left(x\right)=x^2-5$$  

• $$g\left(x\right)=x^2+5$$  

• $$g\left(x\right)=\left(x-5\right)^2$$  

• $$g\left(x\right)=\left(x+5\right)^2$$  

Multiple Choice

$$g\left(x\right)=f\left(x\right)-4$$   Describe the transformation to  $$f\left(x\right)$$   that results in  $$g\left(x\right)$$  .

• $$f\left(x\right)$$  has been translated down 4.

• $$f\left(x\right)$$  has been translated up 4.

• $$f\left(x\right)$$   has been translated 4 units the left

• $$f\left(x\right)$$  has been translated 4 units to the right

Multiple Choice

$$g\left(x\right)=f\left(x-4\right)$$   Describe the transformation to  $$f\left(x\right)$$   that results in  $$g\left(x\right)$$  .

• $$f\left(x\right)$$   has been translated down 4.

• $$f\left(x\right)$$   has been translated up 4.

• $$f\left(x\right)$$   has been translated 4 units the left

• $$f\left(x\right)$$   has been translated 4 units to the right

Multiple Choice

$$g\left(x\right)=f\left(x+4\right)$$   Describe the transformation to  $$f\left(x\right)$$   that results in  $$g\left(x\right)$$  .

• $$f\left(x\right)$$  has been translated down 4.

• $$f\left(x\right)$$  has been translated up 4.

• $$f\left(x\right)$$   has been translated 4 units the left

• $$f\left(x\right)$$  has been translated 4 units to the right

Multiple Choice

$$g\left(x\right)=f\left(x\right)+4$$   Describe the transformation to  $$f\left(x\right)$$   that results in  $$g\left(x\right)$$  .

• $$f\left(x\right)$$  has been translated down 4.

• $$f\left(x\right)$$  has been translated up 4.

• $$f\left(x\right)$$   has been translated 4 units the left

• $$f\left(x\right)$$  has been translated 4 units to the right

Dropdown

 Describe the transformation to  $$f\left(x\right)$$   that results in  $$g\left(x\right)$$  .



$$g\left(x\right)=f\left(x\right)+4$$ $$\rightarrow$$ ​

Select answer

$$g\left(x\right)=f\left(x\right)-4$$ $$\rightarrow$$ ​

Select answer

​

​Multiple Transformations Example: Vertical and Horizontal Translation

​The graph of f(x) was translated 5 units right and 4 units down to create the graph of g(x).

Dropdown

The function $$f(x)=x^2$$ was transformed to create the function  $$g(x)=f(x−2)+5$$ . Complete the sentence about this transformation. 

 Choose the correct answer from each drop-down box to complete the sentence.

The graph of $$f$$ is translated 2 units ​

Select answer

and 5 units ​

Select answer

to create the graph of $$g$$ .

Dropdown

The function $$f(x)=x^2$$ was transformed to create the function  $$g(x)=f(x+2)-5$$ . Complete the sentence about this transformation. 

 Choose the correct answer from each drop-down box to complete the sentence.

The graph of $$f$$ is translated 2 units ​ ​

Select answer

and 5 units ​ ​

Select answer

to create the graph of $$g$$ .

Dropdown

The function $$f(x)=x^2$$ was transformed to create the function  $$g(x)=f(x-8)+5$$ . Complete the sentence about this transformation. 

 Choose the correct answer from each drop-down box to complete the sentence.

The graph of $$f$$ is translated 8 units ​ ​

Select answer

and 5 units ​ ​

Select answer

to create the graph of $$g$$ .

Multiple Choice

If the blue graph is  $$f\left(x\right)=x^2$$  , what is the equation of the red graph?

• $$g\left(x\right)=\left(x+3\right)^2-2$$  

• $$g\left(x\right)=\left(x+2\right)^2-3$$  

• $$g\left(x\right)=\left(x-3\right)^2-2$$  

• $$g\left(x\right)=\left(x-2\right)^2-3$$