https://file.aiquickdraw.com/mathbot/file/1740618941778ax4bepu5.jpg

The graph you've uploaded represents a quadratic function, and the task requires determining the intervals where the function is increasing, decreasing, and constant.

Looking at the graph:
- The function decreases to a minimum point and then increases after that.
- The vertex is likely the lowest point, and from the graph, we can identify the intervals of increasing and decreasing behavior.

### To answer the question:
- The function is **decreasing** to the left of the vertex (where the graph slopes down).
- The function is **increasing** to the right of the vertex (where the graph slopes upward).

### Interval of increasing:
From the graph, the function appears to increase after the vertex. The x-values where this happens are greater than the x-coordinate of the vertex. Let’s say the vertex is at \( x = 3 \). Thus, the interval on which the function is increasing is:
\[
(3, \infty)
\]

Would you like more details on how to analyze the behavior of quadratic functions? Or do you need help with anything else regarding this question?

### Follow-up questions:
1. How do we find the vertex of a quadratic function from the equation?
2. What are the steps to determine where a quadratic function is increasing or decreasing?
3. How can we calculate the rate of change (slope) of a quadratic function at a given point?
4. What is the relationship between the coefficients of a quadratic equation and its graph’s behavior?
5. How do you solve for the intervals of a function’s constancy?

**Tip:** For a parabola, if the coefficient of \( x^2 \) is positive, the function opens upward and increases after the vertex. If it’s negative, the function opens downward and decreases after the vertex.

Determine the intervals on which the function is increasing, decreasing, and constant. List the interval(s) on which the function is increasing.

Learn how to determine the intervals where a quadratic function is increasing or decreasing by analyzing the graph. This problem focuses on identifying the vertex and understanding the shape of the parabola. Suitable for students in Grades 8-10.

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