IXL - Describe transformations of linear and quadratic functions (Algebra 2 practice)

What kind of transformation converts the graph of

(

)

–

into the graph of

(

)

–

translation 1 unit right

translation 1 unit up

translation 1 unit down

translation 1 unit left

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question

What kind of transformation converts the graph of

(

)

–

(

–

)

into the graph of

(

)

–

(

–

)

translation 3 units up

translation 3 units right

translation 3 units down

translation 3 units left

key idea

Transformation of f ( x )	Transformation of graph of f ( x )
f ( x + h )	Translate h units left
f ( x – h )	Translate h units right
f ( x ) + k	Translate k units up
f ( x ) – k	Translate k units down

The vertex form of a quadratic function is

(

)

(

–

)

The vertex is

(

)

solution

Apply the possible translations to

(

)

–

(

–

)

and see which one produces

(

)

–

(

–

)

Translate

(

)

3 units up:

(

)

–

(

–

)

–

(

–

)

This function is not

(

)

Translate

(

)

3 units right:

(

–

)

–

(

–

)

–

(

–

)

This function is not

(

)

Translate

(

)

3 units down:

(

)

–

(

–

)

–

(

–

)

This function is

(

)

So the translation 3 units down of the graph of

(

)

is the graph of

(

)

You could also solve the problem by finding the translation that takes the vertex of

(

)

to the vertex of

(

)

The vertex of

(

)

–

(

–

)

–

(

–

)

(

)

and the vertex of

(

)

–

(

–

)

–

(

–

)

(

)

so the translation 3 units down of the graph

(

)

is the graph of

(

)

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Y.4Transformations of quadratic functions

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