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.
How is the graph f(x) = 2 | x + 3 | - 1 translated from the parent function y = | x |?
If the graph of f(x) = 2 | x + 3 | - 1 is translated 5 units up, what is the new equation?
If f(x) = 2 | x + 3 | - 1 ⇒ k = -1.
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