Quadratic Function: Finding Algebraic Equation for Graph at Point (0,-4)

To solve this problem, let us first note that the labeled point is $(0, -4)$, which suggests the parabola touches or intersects the y-axis at this point. Without more information indicating horizontal translation, it is reasonable to assume this is the vertex of the parabola, pointing down a simple transformation from $y=x^2$ to $y=x^2-4$.

Given the simplicity and symmetry (likely no $x$ coefficient subtracted or added), this directly translates to a parabola form with only a vertical shift downward.

Therefore, the algebraic representation of the given parabolic drawing is $y = x^2 - 4$.

The correct choice corresponding to this is $y = x^2 - 4$.