1.1. A sketch of the graph with equation $y=f(x)$, where $f(x)=({x}^{2}-a{)}^{2}$, with $a>1$ is shown below.

The points $A,B$and $C$ are points where the graph intercepts the coordinate axes.

Write down, in terms of $a$, the coordinates of $A,B$and $C$.

1.2. Sketch the graph of $y=-\frac{1}{2}f(x-1)$, labelling the images of the three points $A,B$and $C$and stating their coordinates in terms of $a$.

1.3. Suggest, in terms of $f(x)$, a combination of at least two transformations, such that the points $A,B$and $C$transform to new positions but remain lying on their respective axes.