Find Decreasing Intervals for y = (x+10)² + 2: Quadratic Function Analysis

To find the intervals where the function $y = (x+10)^2 + 2$ is decreasing, let's proceed as follows:

• Step 1: Recognize that the function is given in vertex form $y = (x+10)^2 + 2$, where the vertex is $(-10, 2)$.
• Step 2: Determine the opening direction of the parabola. Since the coefficient of $(x+10)^2$ is positive (i.e., 1), the parabola opens upwards.
• Step 3: For an upward-opening parabola, the function decreases to the left of the vertex. Thus, as $x$ decreases from $-10$, the function decreases.

Therefore, the function is decreasing in the interval where $x < -10$.

The correct answer is $x < -10$.