The graph in the image is a parabola that opens upwards. Let's determine its domain and range based on the visual information:

Domain:

The domain of a parabola that opens upwards or downwards is all real numbers unless explicitly restricted.

• Domain: $(-\infty, \infty)$

Range:

The range is determined by the lowest (minimum) point of the parabola, which is its vertex.

• From the image, the vertex appears to be at $(0, -5)$.

• The parabola opens upwards, so the $y$-values start from $-5$ and increase indefinitely.

• Range: $[-5, \infty)$

Summary:

• Domain: $(-\infty, \infty)$
• Range: $[-5, \infty)$

Let me know if you need further clarification or details.

Here are some follow-up questions:

1. What is the equation of this parabola if the vertex is known?
2. How would the range change if the parabola opened downwards?
3. What are the x-intercepts of the parabola in this graph?
4. How do we determine the axis of symmetry for this parabola?
5. What transformations (like shifts or stretches) could result in this graph?

Tip: For quadratic graphs, the vertex provides crucial information to determine both the range and symmetry.