Find Increasing Intervals: Analyzing y = (x-4)² - 4

To find the intervals where the function $y = (x - 4)^2 - 4$ is increasing, we proceed as follows:

• Step 1: Identify the vertex of the quadratic function. The given function is in vertex form $y = (x - 4)^2 - 4$, where $h = 4$ and $k = -4$. Thus, the vertex is at $(4, -4)$.
• Step 2: Determine the direction of the parabola. The coefficient of the squared term, $a$, is $1$. Since $a > 0$, the parabola opens upwards.
• Step 3: Determine where the function is increasing. For a parabola that opens upwards, the function is increasing to the right of the vertex. Hence, the function is increasing for $x > 4$.

In conclusion, the function $y = (x-4)^2-4$ is increasing for the interval $x > 4$.

Therefore, the solution to the problem is $x > 4$.