Find Decreasing Intervals of y = (x-6)(x+6): Quadratic Function Analysis

To determine where the function $y = (x-6)(x+6)$ is decreasing, we analyze the quadratic function in its factored form.

Step 1: Identify the roots and the vertex.

• The roots of the function are $x = 6$ and $x = -6$.
• The vertex is exactly halfway between these roots, located at $x = \frac{6 + (-6)}{2} = 0$.

Step 2: Determine the behavior on each side of the vertex.

• This function represents a standard upward-opening parabola because it can be rewritten as $y = x^2 - 36$, which has a positive leading coefficient.
• The parabola decreases as it approaches the vertex from the left and increases as it moves away to the right. Thus, the function is decreasing for values of $x$ less than the vertex, $x = 0$.

Step 3: State the interval where the function is decreasing.

The function is decreasing on the interval $x < 0$.

The correct solution to the problem, where the function is decreasing, is $x < 0$.