https://file.aiquickdraw.com/mathbot/file/1729480012489iz1fmud2.jpg

The graph in the image shows a downward-opening parabola, indicating a quadratic function. The function is decreasing where the graph slopes downward, to the right of the vertex.

### Steps to determine the interval of decrease:
1. The vertex is located at \( x = 0 \) (where the graph reaches its maximum).
2. The function decreases for values of \( x \) greater than the vertex, i.e., for \( x > 0 \).
3. The decreasing interval starts from \( x = 0 \) and extends to positive infinity.

### Answer:
The function is decreasing on the interval \( (0, \infty) \).

Let me know if you want more details or have any questions.

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Here are some related questions to consider:
1. How can we find the interval of increase for this function?
2. What is the equation of this parabola based on the graph?
3. What is the significance of the vertex in determining where the function decreases?
4. How would the interval of decrease change if the parabola opened upwards?
5. How do we generally find intervals of increase or decrease using calculus?

**Tip:** The derivative of a function can help identify where it is increasing or decreasing by analyzing the sign of the derivative.

Determine the interval(s) for which the function shown in the graph is decreasing.

Learn how to determine the intervals where a quadratic function is decreasing based on its graph. This example covers concepts like the vertex of a parabola, the standard quadratic function form, and interval notation. Suitable for students in Grades 9-10.

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