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Let $f(x)=\left(x-2\right)^2$ and $g(x)=-x^2$.

Which of the following transformations have been applied to $f(x)$ in order to obtain $g(x)$?

Shifted right $2$ units

Shifted left $2$ units

Shifted up $2$ units

Shifted down $2$ units

Vertically stretched by a factor of $2$

Vertically compressed by a factor of $2$