Find Decreasing Intervals for y = (x-4)(x+2): Quadratic Function Analysis

To determine where the function $y = (x-4)(x+2)$ is decreasing, we will first convert the product form to standard form:

Step 1: Expand the function: $y = x^2 - 4x + 2x - 8 = x^2 - 2x - 8$

Step 2: Differentiate the function with respect to $x$ to find the derivative $y'$: $y' = \frac{d}{dx}(x^2 - 2x - 8) = 2x - 2$

Step 3: Determine where the derivative is negative: $2x - 2 < 0$

Step 4: Solve for $x$: $2x < 2$ $x < 1$

Therefore, the function $y = (x-4)(x+2)$ is decreasing for $x < 1$.

This corresponds to choice 2: $x<1$