Finding Domains: y=-(x+7/8)² - 1⅕ Function Analysis

The function $y = -\left(x + \frac{7}{8}\right)^2 - 1\frac{1}{5}$ is represented in vertex form, where the vertex of the parabola is at $x = -\frac{7}{8}$, and the maximum value at the vertex is $y = -1\frac{1}{5}$. Since the parabola opens downwards due to the negative coefficient of the squared term, its maximum value is also its highest possible value, which is a negative number $-1\frac{1}{5}$.

Therefore, the function does not reach any positive value for any real number $x$; it only takes on non-positive values. Consequently, the determination of positive and negative domains is as follows:

• $x < 0$: The function can assume all values since the entire parabola lies below the x-axis, producing a negative range for all $x$.
• $x > 0$: No $x$ can produce a positive $y$ value, resulting in no positive values.

Therefore, the positive and negative domains as concluded from this analysis are:

$x < 0 :$ all $x$

$x > 0 :$ none