Find Decreasing Intervals for the Quadratic Function y=(x+15)²+6

To solve where the function $y = (x+15)^2 + 6$ is decreasing, follow these steps:

• Step 1: Recognize the vertex form of the quadratic $y = (x-h)^2 + k$ where $h = -15$ and $k = 6$. Thus, the vertex is at $x = -15$, $y = 6$.
• Step 2: Understand that this is an upward-opening parabola because the coefficient of the squared term (1) is positive. The function decreases to the left of the vertex.
• Step 3: The decreasing interval is to the left of the vertex $x = -15$. Therefore, the function decreases as $x$ goes from $-\infty$ to $-15$.

Therefore, the function decreases for $x < -15$.

The correct answer choice is: $x < -15$.