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The graph shows a quadratic function, which is represented by a parabola. To determine the **domain** and **range** of the function, let's analyze the graph:

1. **Domain**: The domain of a quadratic function is all the possible values that \( x \) can take. Since the parabola extends infinitely in both the left and right directions, the domain is all real numbers.

   \[
   \text{Domain: } (-\infty, \infty)
   \]

2. **Range**: The range is the set of possible values for \( f(x) \). Based on the graph, the parabola has its minimum point at \( f(x) = 0 \), and the curve opens upwards. This means the function's values start at 0 and go up to infinity.

   \[
   \text{Range: } [0, \infty)
   \]

Thus, the domain is \( (-\infty, \infty) \) and the range is \( [0, \infty) \).

Would you like more details or further clarification? Here are some related questions:

1. How can you find the vertex of a parabola given its equation?
2. What is the general form of a quadratic function?
3. How does the direction in which the parabola opens affect its range?
4. Can we determine the axis of symmetry from this graph?
5. How does completing the square help in finding the vertex of a quadratic function?

**Tip:** The domain of any quadratic function will always be all real numbers, but the range depends on the vertex and whether the parabola opens upwards or downwards.

Se presenta la gráfica de una función cuadrática. Determina su dominio y su rango.

Understand how to determine the domain and range of a quadratic function based on its graph. This problem explains core concepts of quadratic equations and how the direction of the parabola affects the range. Suitable for students in Grades 8-10.

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