The function $g(x)$ you have provided seems to be:

$g(x) = x^2 + 6x - 3$

This is a quadratic function, and it can be analyzed in several ways, such as by finding its roots, vertex, or behavior. Let me know how you'd like to proceed.

Would you like to:

1. Find the roots (solutions) of the equation $g(x) = 0$?
2. Find the vertex of the quadratic function?
3. Discuss the symmetry and shape of the graph (parabola)?
4. Analyze the function's behavior for large values of $x$?
5. Plot the function for better visualization?

Tip: The general form of a quadratic function is $ax^2 + bx + c$, and its graph is always a parabola.