2.6 – Vertical and Horizontal Translations

Translating Functions

• A translation is an operation that shifts a graph horizontally, vertically, or both. The results are a graph of the same size and shape, just in a different position

Y = |x + 2| – 3

(-2 , -3)

Parent Function: the simplest function with the given characteristics

Y = |x + 5| + 8

(-5 , 8)

Y = |x – 8| – 6

(8 , -6)

Y = |x – 7| + 4

(7 , 4)

Y = |x – 4| – 5

(4 , -5)

Y = |2x – 8| + 2

(4 , 2)

Y = |3x + 6| – 3

(-2 , -3)

Is there a formula for graphing absolute value equations???

• Y = |x + 2| – 3• Y = |x + 5| + 8• Y = |x – 8| – 6 • Y = |x – 7| + 4• Y = |x – 4| – 5• Y = |2x – 8| + 2• Y = |3x + 6| – 3• Y = |mx + b| + c

(-2 , -3)(-5 , 8)(8 , -6)(7 , 4)(4 , -5)(4 , 2)(-2 , -3)(- b/m , c)

What is the pattern?

• Y = |mx + b| + c

• What does the m (slope) do to the graph?

(- b/m , c)