Find Decreasing Intervals of y = (x-5)²: Quadratic Function Analysis

To solve this problem and determine the interval where the function $y = (x-5)^2$ is decreasing, follow these steps:

• Step 1: Identify the vertex of the parabola. The function is in vertex form $y = (x-5)^2$, meaning the vertex is at $(5, 0)$.
• Step 2: Understand the behavior of the parabola. This parabola opens upwards because there is no negative sign before the $(x-5)^2$, indicating that it decreases on the interval left of the vertex.
• Step 3: Determine the interval where the function is decreasing. Since the parabola opens upwards, it decreases for $x < 5$.

Therefore, the function $y = (x-5)^2$ is decreasing on the interval $x < 5$.