Calculate Area: Finding Descending Region of y=-(x+3)²-10

Find the descending area of the function

$y=-(x+3)^2-10$

To solve this problem, we'll identify the vertex of the given parabolic function and determine on which side of the vertex the function decreases.

Step 1: Identify the Vertex
The function $y = -(x+3)^2 - 10$ is in the vertex form $y = a(x-h)^2 + k$. Here, $a = -1$, $h = -3$, and $k = -10$. Thus, the vertex of the parabola is at $(-3, -10)$.

Step 2: Analyze Parabola's Direction
Since $a = -1$ (a negative value), the parabola opens downwards. For downward-opening parabolas, the function decreases to the right of its vertex.

Step 3: Determine the Decreasing Domain
Since the parabola decreases for values of $x$ greater than the x-coordinate of the vertex, it decreases when $x > -3$.

Therefore, the descending area of the function is $-3 < x$.

The correct answer, corresponding to the choices given, is choice 3: $-3 < x$.