In order to find the function rule for $g(x)$, which is a translation of the parent function $f(x) = x^2$, we can use the general form of a translated quadratic function:

$g(x) = a(x - h)^2 + k$

Where:

• $a$ represents a vertical stretch or compression and reflection.
• $h$ represents a horizontal shift (left or right).
• $k$ represents a vertical shift (up or down).

To determine $a$, $h$, and $k$, we need to analyze the graph of $g(x)$. Since you mentioned the graph, could you please upload it? That will allow me to extract the necessary information to write the function rule accurately.