We want to describe how to transform the parent function y=x2 to the graph of the given quadratic function. y=-(2x)2 To do so, we need to consider two possible transformations.
Let's consider them one at the time.
In the given exercise, x is multiplied by 2. Therefore, the previous graph will be horizontally shrunk by a factor of 21.
Whenever x2 is multiplied by a negative number, we will have a reflection of the graph across the x-axis.
Note how each x-coordinate stays the same, and how each y-coordinate changes its sign.
Let's now graph the given function and the parent function f(x)=x2 on the same coordinate grid.
Finally, let's summarize all the transformations of the graph of f.