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.