To determine the domain and range of the quadratic function based on the graph provided:

1. Domain: The domain of a function represents all possible values of $x$. From the graph, the curve extends from $x = -2$ to $x = 8$, so the domain is the interval $[-2, 8]$.

2. Range: The range represents all possible values of $y$. The graph shows that the highest point (vertex) of the parabola is at $y = 5$, and the parabola opens downward. The lowest value of $y$ continues downward to negative infinity. Therefore, the range is $(-\infty, 5]$.

Thus, the correct answers are:

• Domain: $[-2, 8]$
• Range: $(-\infty, 5]$

Would you like further clarification on this or related concepts?

Relative Questions:

1. How do you determine the vertex of a parabola from a quadratic function?
2. What happens to the domain and range when a parabola opens upward instead of downward?
3. How does the axis of symmetry of a parabola relate to its domain and range?
4. Can the domain of a quadratic function ever be limited in real-life situations?
5. How can you find the domain and range of a function algebraically without graphing it?

Tip: For a quadratic function, the domain is often all real numbers unless specified otherwise by constraints in a graph or context.