Absolute Value Function Transformations

If "a" is positive the function opens up

If "a" is negative, it is a reflection, meaning it opens down

"a" is the slope of the branches of the graph

The larger the "a" value, the more narrow it is

"h" is a horizontal translation

if |x - h| move the graph to the right "h" units

if | x + h| move the graph to the left "h" units

"k" is a vertical translation

if "k" is positive it moves up

if "k" is negative it moves down

either the highest or the lowest point on the graph

has the coordinates (-h, k) the opposite of h and k

h = -3

k = 7

vertex (-h, K)

The vertex is located at (3, 7)

reflection

slope is 2

horizontal translation 7 units left

vertical translation 3 units down

Identify "a", "h" and "k"

plug those values into y = a |x - h| + k