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The graph displayed on your screen represents a quadratic function, which typically has the form \( y = ax^2 + bx + c \). For this particular function, the graph is a downward-opening parabola. 

A quadratic function is increasing on the interval to the right of its vertex when the parabola opens downwards. From the graph, the vertex appears to be at \(x = 0\). Therefore, the function is increasing on the interval from 0 to positive infinity, which is represented as \( (0, \infty) \).

Would you like to know more details about how this was determined or have any other questions?

Here are some related questions to consider:
1. How do you determine the vertex of a quadratic function from its graph?
2. What happens to the interval of increase if the parabola opens upwards?
3. Can you calculate the exact coordinates of the vertex using the vertex formula?
4. What does the derivative of a quadratic function tell you about its increasing and decreasing intervals?
5. How does the value of the coefficient \(a\) in \( y = ax^2 + bx + c \) affect the shape of the parabola?

**Tip:** When determining intervals of increase or decrease from a graph, always look for changes in the direction of the curve—increasing when it rises, and decreasing when it falls.

On which interval is the function increasing?

Learn how to determine the interval on which a quadratic function is increasing by analyzing its graph. This problem involves key concepts from algebra and graph analysis, suitable for students in Grades 9-12.

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