Find the Area Under y=-(x+2)²+4: Quadratic Function Analysis

Find the descending area of the function

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

To solve this problem, we need to determine where the function $y = -(x+2)^2 + 4$ is decreasing.

First, note that the function is in the vertex form for a parabola, $y = a(x-h)^2 + k$. We identify $a = -1$, $h = -2$, and $k = 4$.

The vertex of this parabola is at $(h, k) = (-2, 4)$. This vertex represents the maximum point of the parabola because $a = -1$ is negative, indicating that the parabola opens downwards.

In a downwards-opening parabola, the function is increasing for values of $x$ less than the vertex $h$, and it is decreasing for values of $x$ greater than the vertex $h$.

Therefore, the function is decreasing for $x > -2$.

Thus, the descending area of the function is:
$-2 < x$.

The correct choice amongst the provided answers is:

$-2 < x$