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The graph provided shows a downward-opening parabola, which is characteristic of a quadratic function of the form \( f(x) = ax^2 + bx + c \), where \( a < 0 \).

To determine where the function is increasing, we need to analyze the slope of the curve. A function is increasing on an interval where its derivative is positive (i.e., the slope of the tangent line is positive).

From the graph, the vertex of the parabola occurs at \( x = 0 \), which is the maximum point. The function increases on the left of the vertex, where the curve rises.

**Conclusion:**
The function is increasing on the domain \( (-\infty, 0) \), as the curve rises from negative infinity until it reaches the peak at \( x = 0 \).

Would you like further details on how to find the vertex or analyze the behavior of this quadratic function?

Here are 5 related questions:
1. How can you determine the domain of a quadratic function?
2. What is the significance of the vertex in a parabola?
3. How do you calculate the derivative of a quadratic function?
4. What does it mean for a function to be increasing or decreasing?
5. Can a quadratic function be increasing and decreasing at the same time?

**Tip:** The vertex of a parabola given by \( f(x) = ax^2 + bx + c \) is located at \( x = -\frac{b}{2a} \), which helps identify intervals where the function increases or decreases.

Determine the domain on which the following function is increasing.

Discover how to find the domain where a quadratic function is increasing by analyzing the graph and using derivative rules. Learn about the vertex and intervals of quadratic functions, along with step-by-step solutions. Perfect for Grades 9-12 students studying algebra and calculus.

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