https://file.aiquickdraw.com/mathbot/file/1725541010689iduejuwn.jpg

The image shows a parabola, and the question asks to "Determine the domain on which the following function is increasing."

For a quadratic function in the form of a parabola (like the one in the image), the domain where the function is increasing refers to the interval of x-values where the slope of the curve is positive (the curve is going upward).

### Key Points:
- The parabola opens downward, which means it has a maximum point at its vertex.
- The function increases to the left of the vertex.

#### To solve:
1. **Find the vertex of the parabola**: This will give us the turning point where the function changes from increasing to decreasing.
2. **Determine the domain where the function is increasing**: This will be for x-values less than the x-coordinate of the vertex.

If you provide the specific coordinates or more details about the graph, I can pinpoint the exact domain.

Would you like to provide further details or ask more questions related to this?

### Related Questions:
1. How do you find the vertex of a quadratic function algebraically?
2. Can you explain the difference between the domain and the range of a function?
3. What are the characteristics of a function that is increasing or decreasing?
4. How does the concavity of a parabola affect where it's increasing or decreasing?
5. How can the first derivative help in determining where a function increases or decreases?

### Tip:
For a parabola, the x-coordinate of the vertex can be found using the formula \(x = -\frac{b}{2a}\), where the quadratic equation is in the form \(ax^2 + bx + c\).

Determine the domain on which the following function is increasing.

Learn how to determine the domain where a quadratic function is increasing by analyzing a parabola. This tutorial explains how to find the vertex and identify the increasing interval using the quadratic formula. Suitable for students in Grades 9-11.

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