The question appears to be asking on which interval the given quadratic function, $y = x^2 - 4x - 5$, is increasing.

To solve this, let's follow these steps:

1. Find the derivative of the function $y = x^2 - 4x - 5$ because the derivative of a function gives us the rate of change of that function. For a quadratic function, it shows whether the function is increasing or decreasing.

   The derivative is: $\frac{dy}{dx} = 2x - 4$

2. Set the derivative equal to zero to find the critical points: $2x - 4 = 0$ Solving for $x$: $x = 2$ This critical point is where the function changes from decreasing to increasing or vice versa.

3. Analyze the sign of the derivative to determine where the function is increasing:

   • For $x > 2$, the derivative $2x - 4$ is positive, meaning the function is increasing.
   • For $x < 2$, the derivative is negative, meaning the function is decreasing.

Thus, the function increases for $x > 2$.

Therefore, the correct interval where the function is increasing is $(2, +\infty)$, which corresponds to option b.

Do you need further clarification on this solution?

Here are some related questions:

1. How can you tell if a quadratic function is increasing or decreasing?
2. What is the significance of the vertex in a quadratic function?
3. How do you find the critical points of a function?
4. What happens to a quadratic function as $x \to \pm\infty$?
5. How can you use the second derivative to determine concavity?

Tip: To quickly determine where a quadratic function is increasing or decreasing, find the derivative and analyze the sign of the derivative around the critical points.