We want to describe the transformation of the parent function represented by the quadratic function To do so, we need to consider two possible transformations.
Let's consider them one at a time.
If an addition or subtraction is applied to only the variable, the graph will be horizontally translated. In case of addition, the graph will be translated to the left. In case of subtraction, it will be moved to the right. In the given equation, is being added to so the graph of the parent function will be translated units to the left.
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, is subtracted from the whole function, so the previous graph will be translated units down.
Let's now graph the given function and the parent function on the same coordinate plane.
We see that the graph of is a translation units to the left and units down of the graph of