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

Find the negative area of the function

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

To find the negative area for the function $y = -(x+4)^2$, consider when the function is negative or equals zero:

• The parabola $y = -(x+4)^2$ opens downward with the vertex at $x = -4$, when $x = -4$, $y = 0$.
• For $x \neq -4$, the expression $-(x+4)^2$ is negative because $(x + 4)^2$ is always positive or zero, and the negative sign flips it to non-positive, i.e., negative unless zero.
• Hence, everywhere except at the vertex $x = -4$, the function is negative.

The function $y = -(x+4)^2$ is negative for every point except where $x = -4$.

Therefore, the correct answer from the choice given is: For each $x \neq -4$.