The given function is:

$g(x) = x^2 + 6$

This function resembles the parent function of the quadratic family, which is:

$f(x) = x^2$

The parent function $f(x) = x^2$ is a basic quadratic function, which is a parabola with its vertex at the origin (0, 0).

In the function $g(x) = x^2 + 6$, the graph of $f(x) = x^2$ is shifted upward by 6 units due to the "+6" constant. This is a vertical translation.

Answer: The parent function is $f(x) = x^2$.

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Would you like a more detailed explanation of how this shift works? Or do you have any other questions? Here's a list of related topics you might find helpful:

1. What is the effect of vertical translations on a function?
2. How do you graph quadratic functions?
3. What are the characteristics of a parent quadratic function?
4. How does a transformation of functions impact the graph?
5. What is the general form of a quadratic function?

Tip: Always look for constants added to the function to identify vertical translations in transformations.