Find Increasing Intervals: Analyzing y = -(x-12)² - 4

To solve this problem, we'll determine where the function $y=-(x-12)^2-4$ is increasing:

First, recognize that this function is a quadratic equation in vertex form:

• The standard form of a quadratic in vertex form is $y=a(x-h)^2+k$.
• In our case, $a = -1$, $h = 12$, and $k = -4$.

Since $a = -1$, which is less than zero, the parabola opens downward. This implies:

• The function is increasing before reaching its vertex.
• The vertex, given by $x = h$, is $x = 12$.

The function is increasing on the interval where $x < 12$ because:

• The function decreases after passing the vertex $x = 12$.
• Therefore, for values of $x$ less than 12, the function increases.

Therefore, the interval where the function is increasing is $x < 12$.