https://file.aiquickdraw.com/mathbot/file/1727280299869yzhcdvuq.jpg

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.

Find the range and domain of the quadratic function with vertex (3, 0) and the graph shown.

Explore how to determine the domain and range of a quadratic function with its vertex at (3, 0) and opening downward. The domain is all real numbers, and the range is (-∞, 0]. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation