Find Decreasing Intervals of y = -(x-14)² - 6: Vertex Form Parabola Analysis

To solve this problem, we'll follow these steps:

• Step 1: Identify the given function and its form.
• Step 2: Determine the vertex of the quadratic function.
• Step 3: Analyze the function intervals based on the opening direction of the parabola.

Now, let's work through each step:

Step 1: The function is given in the vertex form as $y = -(x-14)^2 - 6$, which identifies $a = -1$, $h = 14$, and $k = -6$.

Step 2: The vertex of this quadratic function is $(14, -6)$.

Step 3: Because $a < 0$ (the coefficient of $(x-h)^2$ is negative), the parabola opens downwards. This means:

• The function is increasing to the left of the vertex, specifically for $x < 14$.
• The function is decreasing to the right of the vertex, specifically for $x > 14$.

Therefore, the function $y = -(x-14)^2 - 6$ is decreasing for $x > 14$.