IXL - Translations of functions (Algebra 2 practice)

The graph shows

(

)

which is a translation of

(

)

Write the function rule for

(

)

Write your answer in the form

–

where

and

are integers or simplified fractions.

(

)

ref_doc_title.

Learn with an example

question

The graph shows

(

)

which is a translation of

(

)

Write the function rule for

(

)

Write your answer in the form

(

–

)

where

and

are integers or simplified fractions.

(

)

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

solution

First, recall the graph of the base function

(

)

Both

(

)

and

(

)

are parabolas. If a parabola is translated

units horizontally and

units vertically, every point on the graph is translated by that rule, including the vertex. So, you can look at the vertices to find the translation rule.

The vertex of

(

)

(

)

The vertex of

(

)

(

)

To translate

(

)

(

)

move 3 units right.

The function

translated 3 units right is

(

)

So, the equation of

(

)

is:

(

)

(

–

)

Looking for more? Try these:

Lesson: Absolute value functions

Lesson: Quadratic functions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

H.3Graph an absolute value function

N.5Graph a quadratic function

W.1Function transformation rules

M.8Evaluate a function: plug in an expression

Lesson: Absolute value functions

Lesson: Quadratic functions

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