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The question asks to determine the open interval on which the function shown in the graph is increasing.

From the graph, we can see the function is a parabola that opens downwards. A parabola of this form decreases to its vertex and then increases after that point.

To determine the interval of increase:
- The graph increases after the vertex, which is at \( x = -2 \). 
- The function increases for values of \( x > -2 \).

Thus, the function is increasing on the interval \( (-2, \infty) \).

The correct choice is:
- **A**: The function is increasing on the interval \( (-2, \infty) \).

Would you like more details or have any further questions?

Here are 5 related questions for deeper understanding:
1. How can you find the vertex of a parabola from its equation?
2. What is the difference between open and closed intervals in interval notation?
3. How do you determine where a function is decreasing?
4. How do you graph quadratic functions based on their vertex form?
5. What role does the leading coefficient play in determining the direction a parabola opens?

**Tip**: When analyzing graphs for increasing and decreasing intervals, focus on the slope—whether it is positive (increasing) or negative (decreasing).

Use the graph to determine open interval on which the function is increasing, if any.

This page explains how to determine the increasing intervals of a quadratic function from its graph, focusing on understanding the behavior of parabolas. Learn to identify the vertex and use it to find where the function is increasing, suitable for high school students.

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