https://file.aiquickdraw.com/mathbot/file/1725927813140nz4eo0vc.jpg

The graph depicts a parabola opening downwards, indicating a quadratic function. To determine where the function is decreasing, we need to look at the portion of the graph where the slope is negative (falling).

The graph reaches its maximum value at the vertex, which occurs at \(x = 1\), where the function changes from increasing to decreasing. From this point onward, as \(x\) increases, the function is decreasing.

Thus, the function is decreasing for \(x > 1\), and looking at the graph, it decreases indefinitely towards the right, i.e., from \(x = 1\) to \(+\infty\).

Therefore, the interval where the function is decreasing is:

\[
(1, \infty)
\]

Would you like more details or have any questions about this explanation?

Here are 5 related questions:
1. What is the interval where the function is increasing?
2. How do you find the vertex of a parabola algebraically?
3. What is the significance of the vertex in a quadratic function?
4. How do you determine intervals of increase or decrease from a graph without calculus?
5. Can you identify the equation of this parabola from its graph?

**Tip:** When analyzing functions, the vertex of a parabola is a key point, marking the transition between increasing and decreasing intervals.

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

Determine the interval where the quadratic function is decreasing by analyzing the graph. Learn about vertex and how to find increasing and decreasing intervals.

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