The graph shows a quadratic function with its vertex at $(3, 0)$, and it opens downward.

Domain:

• The domain of a quadratic function is always all real numbers unless there are restrictions, which is not the case here. So, the domain is: $(-\infty, \infty)$

Range:

• The vertex is at $(3, 0)$, and since the parabola opens downward, the maximum value occurs at $y = 0$. The function can take any value less than or equal to 0. Hence, the range is: $(-\infty, 0]$

Let me know if you need further explanation, or if you'd like to discuss any of these points.

Relative Questions:

1. What is the general form of a quadratic function, and how does it relate to its graph?
2. How do you determine if a quadratic opens upwards or downwards based on its equation?
3. How can the vertex of a quadratic function be found from its equation in standard form?
4. What is the significance of the domain and range in real-world applications of quadratic functions?
5. How do transformations like shifting and scaling affect the domain and range of a function?

Tip:

Always remember, for a parabola, the domain is typically all real numbers unless specific constraints are provided. The range is influenced by the vertex and the direction the parabola opens.