Find Increasing Intervals for y = -(x+10)² - 4: Quadratic Function Analysis

To identify the intervals where the function $y = -(x+10)^2 - 4$ is increasing, we must first determine the nature and axis of symmetry of this parabola.

Given that the function is in vertex form, $y = a(x-h)^2 + k$, we know the vertex of this parabola is at $(h, k)$. For our function:

• The vertex is $(-10, -4)$ from the formula $y = -(x+10)^2 - 4$.
• Since the coefficient of the quadratic term $a = -1$ is negative, the parabola opens downwards.

For downward-opening parabolas, the function increases to the left of the vertex and decreases to the right of the vertex.

Therefore, the function $y = -(x+10)^2 - 4$ is increasing for values of $x$ less than the x-coordinate of the vertex. Hence, the interval of increase is where $x < -10$.

In conclusion, the interval where the function is increasing is $x < -10$.