To find the function rule for $g(x)$, which is a translation of $f(x) = x^2$, we use the vertex form of a quadratic function:

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

Here, the vertex $(h, k)$ is given as $(8, 0)$. Substituting $h = 8$ and $k = 0$ into the equation, we have:

$g(x) = a(x - 8)^2$

Now, to find $a$, we need another point on the graph of $g(x)$. If the graph passes through a known point, substitute its coordinates $(x, g(x))$ into the equation to solve for $a$.

Example Calculation (Assume a Point):

If you provide an additional point on $g(x)$, I can compute $a$ and complete the equation. Otherwise, the general form based on the vertex is:

$g(x) = a(x - 8)^2$

Would you like to provide more information or ask questions? Here are some expanding inquiries:

1. What point on the graph besides the vertex is provided?
2. Does the graph open upwards or downwards (sign of $a$)?
3. Is there information about the slope or shape of $g(x)$?
4. Are there any specific transformations of $f(x) = x^2$ described?
5. Should $a$ remain in terms of a fraction or decimal?

Tip: If you know the direction and another point on the graph, solving for $a$ becomes straightforward.