The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
Since the graph of f(x) = x^2 was translated 6 units to the left to create the graph of g, the vertex of g is at the point (h - 6, k).
The vertex of f(x) = x^2 is at (0, 0), so the vertex of g is at (-6, 0).
Since the vertex is at (-6, 0), the equation of g in vertex form is:
g(x) = a(x + 6)^2 + 0
We can find the value of "a" by using another point on the parabola. For example, if we know that g(-3) = 9, then we can substitute these values into the equation and solve for "a":
9 = a(-3 + 6)^2
9 = 9a
a = 1
So the equation of g in vertex form is:
g(x) = (x + 6)^2