**Given the quadratic equation**

**which has the following graph**

**I want to replace x with x - 4. In order
to clearing see the affect of this replacement before I graph
the resulting equation, I will rewrite my original equation in
graphing form:**

**Now, I replace x with x - 4.**

**So,**

**It is clear to see that replacing x with
x - 4 will result in a horizontal translation (4 units) of the
original equation. The translation vector is <4,0>.**

**By overlaying the graphs, we confirm that
the new graph is a horizontal translation of the original graph.**

**To move the graph of the original equation
to the second quadrant, ****click here.**

**To change the equation to produce a graph
concave down that shares the same vertex, ****click here.**