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.