Finding Increasing Intervals: Analyze y = (x+10)² + 2

To solve this problem, we will determine where the given quadratic function is increasing.

• Step 1: Identify the vertex. The function $y = (x+10)^2 + 2$ is in vertex form $y = a(x-h)^2 + k$, where $h = -10$. Therefore, the vertex is at $x = -10$.
• Step 2: Determine the behavior of the parabola. Because the coefficient of $(x+10)^2$ is positive (specifically, $a = 1$), the parabola opens upwards.
• Step 3: Identify intervals of increase and decrease. Since the parabola opens upwards, it decreases to the left of the vertex and increases to the right of the vertex.

Therefore, the function is increasing for $x > -10$.

Thus, the interval where the function is increasing is $x > -10$.