Calculate Negative Area: Finding Area Below y=-(x+3)²-4

Find the negative area of the function

$y=-(x+3)^2-4$

The function given is $y = -(x+3)^2 - 4$. This function represents a parabola opening downwards, with the vertex at $(-3, -4)$. Because $y = -(x+3)^2 - 4$ is a downward-opening parabola with a vertex below the x-axis at -4, it means every point on the parabola has a y-value less than zero. Thus, for all values of $x$, the function is negative.

The entire graph of this quadratic function lies below the x-axis; therefore, any form of "area" discussed here would necessarily be negative since the function never crosses into positive y-values (it is not asking for the integration under the curve relative to x-axis as such).

Consequently, the situation describes that the parabola completely lies under the x-axis across its domain: for all real $x$.

Therefore, the solution to the problem is: For all $x$, the area is negative.