https://file.aiquickdraw.com/mathbot/file/1730998419776awi25pnz.jpg

To determine the domain on which this function is decreasing, we observe the graph. The function appears to be a parabola opening upwards, indicating a quadratic function. For a parabola of this nature, the function is decreasing on the left side of the vertex (the lowest point) and increasing on the right side of the vertex.

In this graph:
1. The vertex of the parabola is at \( x = 0 \).
2. The function decreases as \( x \) moves from \( -\infty \) to \( 0 \).

Thus, the domain on which the function is decreasing is:
\[
(-\infty, 0)
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you determine the vertex of a parabola from its equation?
2. What characteristics of a quadratic function indicate where it increases or decreases?
3. Can a function have multiple intervals of increase and decrease?
4. How can the first derivative test confirm intervals of increase or decrease?
5. What is the significance of the axis of symmetry in determining where a function is increasing or decreasing?

**Tip:** For quadratic functions, identifying the vertex is key to determining intervals of increase and decrease.

Determine the domain on which the following function is decreasing.

Analyze a quadratic function to find the interval where it is decreasing. Learn about vertex identification and interpreting function behavior from graphs. Suitable for Grades 9-10 math students.

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