Transformations of f(x): Translation 11 units down.
Practice makes perfect
We want to describe how the graph of the given quadratic function is related to its parent function f(x)=x^2. To do so we will transform f(x)=x^2 to the graph of the given function.
g(x)=x^2-11
In order to do this, we need to consider the only possible transformation. In this case it's vertical translation.
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, 11 is subtracted from the whole function, so the graph will be translated 11 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.
