https://file.aiquickdraw.com/mathbot/file/1729468356201n515miye.jpg

The graph you uploaded shows a parabolic curve, which is symmetric about the y-axis and opens downward.

### Domain:
The domain of a function refers to all the possible values of \(x\) for which the function is defined. In this case, the parabola extends infinitely to the left and right along the x-axis, meaning the function is defined for all real numbers.

- **Domain**: \( (-\infty, \infty) \)

### Range:
The range refers to all the possible values of \(y\) that the function can take. Since the parabola opens downward, it has a maximum value at the vertex, and the graph extends downwards infinitely. The highest point on the graph (the vertex) appears to be at \(y = 0\), and it decreases without bound.

- **Range**: \( (-\infty, 0] \)

### Final Answer:
- **Domain**: \( (-\infty, \infty) \)
- **Range**: \( (-\infty, 0] \)

Do you want more details or explanations on this?

Here are five questions to consider:
1. How do you find the vertex of a parabola algebraically?
2. What would change about the domain and range if the parabola opened upwards?
3. How would you express the domain and range in set-builder notation?
4. How do transformations (translations, reflections) affect the domain and range of parabolas?
5. How can you determine the equation of the parabola from the graph?

**Tip**: The domain of most parabolas is all real numbers unless there are specific restrictions (like a real-world scenario limiting \(x\)).

Determine the domain and range of the graph. Express your answer in interval notation.

Learn how to find the domain and range of a quadratic function by analyzing its graph. This example demonstrates the solution step by step, providing insights into parabolas, interval notation, and the properties of quadratic functions. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation