Absolute value graphs (Transformation)

Refer to Khan academy: Absolute value graphs

To understand this idea, need to review the previous knowledge of Transformation of graphs, including translation, rotation, reflection, dilation. Also need to know the scale factor of dilation.

For a simplest form of an absolute value equation, it can be represented as:

And the most common use for this idea, is in Quadratic:
y=x²

And the general form of an absolute value equation:

In the equation,

• The sign of a, negative sign of a means the graph is flipped by x-axis.
• a is the scale factor of the graph, equals to g'(x)÷g(x).
• h is distance of moving right, should be subtracted by x.
• k is distance of moving up, should be added by y.

Notice that:
The h is confusing sometime ----
it's the distance of moving right,
and should be subtracted from x.
Subtracted ,subtracted, subtracted!
For understanding why is it subtracted, review this Khan lecture in 2 minutes.

Simplest equation y = |x|

Shifted(Translated) equation y = |x + h| + k

Flipped(Reflected) version y = - |x|

It’s only flipping by the x axis.

Scaled(Dilated) equation y = a |x|