https://file.aiquickdraw.com/mathbot/file/1726883322422orwnn1lj.jpg

The graph you’ve uploaded shows a parabola that appears to open upwards. Let's break down the intervals where the function is **decreasing**, **increasing**, and **constant** based on the curve:

1. **Decreasing interval**: This is the portion of the graph where the function is going downhill (as the \( x \)-values increase, the \( y \)-values decrease). From the graph, this happens to the left of the vertex.
   
   - The vertex is at \( x = 0.3 \).
   - So, the function is decreasing on the interval \( (-\infty, 0.3] \).

2. **Increasing interval**: This is the portion where the graph is going uphill (as the \( x \)-values increase, the \( y \)-values increase). This happens to the right of the vertex.
   
   - The function is increasing on the interval \( [0.3, \infty) \).

3. **Constant interval**: The function is never constant because it's a smooth curve and changes direction only at the vertex.

To summarize:
- **Decreasing**: \( (-\infty, 0.3] \)
- **Increasing**: \( [0.3, \infty) \)
- **Constant**: None

Would you like further details or have any questions about this? 

Here are 5 related questions:
1. How do you determine the vertex of a parabola from its equation?
2. What are the properties of the graph of a quadratic function?
3. How can you calculate the axis of symmetry from a quadratic equation?
4. What role does the vertex play in understanding the intervals of increase and decrease?
5. How can you find the maximum or minimum value of a quadratic function?

**Tip**: The vertex of a parabola represents either the maximum or minimum point, depending on whether the parabola opens upwards or downwards!

Determine the intervals over which the function is decreasing, increasing, and constant.

Explore how to determine the intervals where a parabolic function is increasing, decreasing, or constant. This guide covers essential concepts like vertex calculation and function behavior, suitable for high school level study.

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