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Find the open interval(s) where the following function is increasing, decreasing, or constant. Express your answer in interval notation.

The graph shown appears to be a parabola that opens upwards, representing a quadratic function. We can determine where the function is increasing or decreasing based on the behavior of the graph.

### Analyzing the Graph:
1. **Decreasing Interval**: 
   The function is decreasing as the graph slopes downwards from the left side towards the vertex. This happens from \( x = -\infty \) to the vertex at \( x = 0 \).

2. **Increasing Interval**: 
   The function starts increasing after the vertex at \( x = 0 \), as the graph slopes upwards. This happens from \( x = 0 \) to \( x = \infty \).

3. **Constant Interval**: 
   There is no interval where the function is constant because the graph is either increasing or decreasing everywhere.

### Intervals in Notation:
- The function is **decreasing** on the interval \( (-\infty, 0) \).
- The function is **increasing** on the interval \( (0, \infty) \).
- There is **no constant** interval.

Would you like any further explanation or details on this? Here are some related questions you might find useful:

1. How do you find the vertex of a quadratic function algebraically?
2. What is the importance of the derivative in determining increasing and decreasing intervals?
3. Can a quadratic function have more than one increasing and decreasing interval?
4. How does the leading coefficient of a quadratic equation affect the direction of the parabola?
5. What are the implications of symmetry in the graph of a quadratic function?

**Tip**: The vertex of a parabola is a critical point where the function changes from increasing to decreasing or vice versa.

Learn how to find the increasing and decreasing intervals of a quadratic function based on its graph. This example walks you through the steps to identify the behavior of the function in different regions, focusing on the intervals where the function rises or falls. Ideal for students in Grades 9-11.

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