Find the Domain of Increase for y = -x² - 8x - 20

To find the domain of increase for the function $y = -x^2 - 8x - 20$, we need to determine the vertex of the parabola, as it will partition the function into increasing and decreasing intervals.

The vertex $x$-coordinate for the quadratic function $y = ax^2 + bx + c$ is given by the formula $x = -\frac{b}{2a}$.

Here, $a = -1$, and $b = -8$.

Substitute these values into the vertex formula:

$x = -\frac{-8}{2 \times -1} = \frac{-8}{-2} = 4$.

Thus, the vertex occurs at $x = -4$.

Since the parabola opens downwards (as $a = -1$ is less than zero), the function is increasing to the left of the vertex. Therefore, the domain of increase is $x < -4$.

Thus, the domain of increase for the function is $x < -4$.