In this section, all the transformations will be presented together.

It is important to be able to identify how each parameter in the vertex form equation affects the graph.

### Example

How is the graph f(x) = 2 | x + 3 | - 1 translated from the parent function y = | x |?

• a = 2 is a reflection across the x-axis, a stretch creating a narrow graph
• h = -3 is a horizontal translation, moving the graph to the left three units
• k = -1 is a vertical translation, moving the graph down one unit

If the graph of f(x) = 2 | x + 3 | - 1 is translated 5 units up, what is the new equation?

• A translation of 5 units up is vertical and affects ONLY the k in the equation.
• If f(x) = 2 | x + 3 | - 1 ⇒ k = -1.

• To translate this graph up, you should add to “k”.
• Starting at -1 and moving up 5 units, gives you -1 + 5 = 4, so the new h = 4.

The new equation is: f(x) = 2 | x + 3 | + 4

The new graph is:

The tables of values for the two equations are:

f(x) = 2 | x + 3 | − 1

 x y 0 5 -1 3 -3 -1 -5 3 -6 5

and

**Vertex

f(x) = 2 | x + 3 | + 4

 x y 0 10 -1 8 -3 4 -5 8 -6 10

**Vertex