We will start with the graph of the standard/parent function \(\displaystyle{y}={x}^{{{2}}}\)

When we shift the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) by k units to the right, we get the graph of \(\displaystyle{y}={f{{\left({x}-{k}\right)}}}\)

Therefore, the graph of \(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\) is obtained by shifting the graph of \(\displaystyle{y}={x}^{{{2}}}\) by 3 units to the right.

In the graph below:

The blue dashed parabola represents \(\displaystyle{y}={x}^{{{2}}}\)

The black solid parabola represents \(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\)

When we shift the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) by k units to the right, we get the graph of \(\displaystyle{y}={f{{\left({x}-{k}\right)}}}\)

Therefore, the graph of \(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\) is obtained by shifting the graph of \(\displaystyle{y}={x}^{{{2}}}\) by 3 units to the right.

In the graph below:

The blue dashed parabola represents \(\displaystyle{y}={x}^{{{2}}}\)

The black solid parabola represents \(\displaystyle{y}={\left({x}-{3}\right)}^{{{2}}}\)