Transformations: Translation six units down Graph:
We want to describe how to transform the parent function f(x)=x^2 to the graph of the given quadratic function.
g(x)=x^2-6
To do so, we need to consider four possible transformations.
Notice that we only need to consider the fourth transformation.
Vertical Translation
If an addition or subtraction is applied to the whole function, the graph will be vertically translated. In the case of addition, the graph will be translated up. In the case of subtraction, it will be moved downwards. In the given equation, 6 is subtracted from the whole function, so the parent function graph will be translated six units down.
Final Graph
Let's now graph the given function and the parent function f(x)=x^2 on the same coordinate grid.
Finally, let's summarize how to draw the graph of the given function when starting with the parent function, f(x)=x^2.
