Find Intervals of Increase and Decrease: Analyzing y = -(4x+32)²

To determine the intervals of increase and decrease, follow these steps:

• Step 1: Simplify the function. The given function is $y = -(4x + 32)^2$, a quadratic in terms of $x$.
• Step 2: Recognize that this is a downward-facing parabola because the coefficient of $(4x + 32)^2$ is negative.
• Step 3: Find the vertex or the critical point of the parabola. The function is in the form $y = -a(x + h)^2 + k$. Here, $a = 4$, $h = -8$, and $k = 0$.
• Step 4: The vertex occurs at $x = -8$. The function is symmetrical about this point.
• Step 5: Since it's a downwards-opening parabola, the function increases on the left of the vertex and decreases on the right of the vertex.
• Step 6: Thus, the function decreases ($\searrow$) for $x < -8$ and increases ($\nearrow$) for $x > -8$.

Consequently, the intervals of increase and decrease are:
Decreasing: $x < -8$
Increasing: $x > -8$

Therefore, $\searrow: x<-8 \\ \nearrow: x>-8$ is the correct answer.