Graph comparison of two functions.

Question

$f(x) = x^2$ and $g(x) = x^2 - 6x +4$

In relation to $f$, the graph $g$ is shifted ...? The answer is given to be $3$ units to the right and $5$ units down. How?

Answer 1

Write $x^2-6x + 4$ as $(x-3)^2-5$. The $\color{red}{-3}$ indicates the shift to the right, and the $\color{blue}{-5}$ indicates the shift down.

Answer 2

Hint:

$$ (y+5)=(x-3)^2 \iff y=x^2-6x+4 $$

You can see the translation?