https://file.aiquickdraw.com/mathbot/file/1726688731094a8p27bc9.jpg

https://file.aiquickdraw.com/mathbot/file/1726688731094lua8vi63.jpg

Looking at the graphs from the images you provided, let's address both questions:

### 1. **Range in Inequality Notation**:
   - The range refers to the possible values of \( y \) for the function (the vertical extent of the parabola).
   - In the first graph, the parabola opens upwards with its vertex at the lowest point, around \( y = -4 \). The parabola continues upwards indefinitely.
   - Therefore, the **range in inequality notation** is:
   \[
   y \geq -4
   \]
  
### 2. **Domain in Inequality Notation**:
   - The domain refers to the possible values of \( x \) for the function (the horizontal extent).
   - Since this is a standard quadratic function, the parabola extends infinitely in both directions along the \( x \)-axis.
   - Therefore, the **domain in inequality notation** is:
   \[
   -\infty < x < \infty
   \]
   
Let me know if you'd like further clarifications or additional details.

### Related Questions:
1. How do you find the vertex of a parabola algebraically?
2. How does the range of a quadratic function change if the parabola opens downwards?
3. What is the general form of a quadratic function?
4. How do you convert a quadratic function from standard form to vertex form?
5. How do you determine if a parabola has a minimum or maximum value?

**Tip**: The range of a quadratic function is always based on the direction the parabola opens (upwards or downwards) and its vertex.

State the Range and Domain in Inequality notation for the given quadratic functions.

Learn how to determine the range and domain of quadratic functions using inequality notation. This lesson covers key algebraic concepts, including identifying the vertex and interpreting the parabola's direction.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation