Find Increasing Intervals for y = -(x+7)² - 5: Quadratic Function Analysis

To find the intervals where the quadratic function $y = -(x+7)^2 - 5$ is increasing, we will analyze the structure of the function.

The function is in the vertex form $y = a(x-h)^2 + k$. Here, $a = -1$, $h = -7$, and $k = -5$. Therefore, the vertex of this parabola is $(-7, -5)$.

Since $a = -1$, which is less than zero, the parabola opens downward. For parabolas that open downward, the function is increasing on the interval to the left of the vertex and decreasing to the right of the vertex.

Consequently, the function is increasing for $x < -7$.

The correct answer is therefore $x < -7$.