To determine the domain and range of the graph, let's analyze the given parabola visually.

Domain:

The domain represents all the possible values of $x$ for which the function is defined.

• The graph extends horizontally from $x = -5$ to $x = 5$.
• Therefore, the domain is the closed interval $[-5, 5]$.

Range:

The range represents all possible values of $y$ that the graph takes.

• The graph reaches its lowest point at $y = 0$ (the vertex) and its highest point is at $y = 10$ (the top of the parabola).
• Therefore, the range is the closed interval $[0, 10]$.

Final answer:

• Domain: $[-5, 5]$
• Range: $[0, 10]$

Would you like further details on how this is derived, or any questions about intervals?

Here are five related questions to deepen your understanding:

1. What are the conditions that define a parabola's domain and range?
2. How do you determine the vertex of a parabola from its graph?
3. What happens to the domain and range if the parabola opens downwards instead?
4. How would the domain and range change if the graph were a different shape, like a circle?
5. Can you describe the difference between open and closed intervals in interval notation?

Tip:

When analyzing graphs, always identify key points like the vertex and the intercepts to determine the domain and range easily.