https://file.aiquickdraw.com/mathbot/file/1724965895762rwopnqkf.jpg

Let's focus on solving the problem you asked about, which is finding the domain and range for the given quadratic function(s) in the image. Based on the visible content, here’s the process for determining the domain and range for quadratic functions:

### 1. **Identifying Domain and Range of Quadratic Functions:**
   A quadratic function generally takes the form \( y = ax^2 + bx + c \), and its graph is a parabola. The domain and range of the function depend on the direction and position of the parabola.

   - **Domain:** The domain of a quadratic function is typically all real numbers, since you can plug any real number into the equation for \( x \) and get a corresponding \( y \) value. Therefore, the domain is:
     \[
     \text{Domain}: (-\infty, \infty)
     \]

   - **Range:** The range depends on the vertex and the direction the parabola opens (upwards or downwards).
     - If the parabola opens upwards, the range starts from the y-coordinate of the vertex and goes to infinity.
     - If the parabola opens downwards, the range starts from negative infinity and goes up to the y-coordinate of the vertex.

### 2. **Analyzing the Specific Quadratic Graphs:**
   The first graph in the image shows a parabola opening upwards with a vertex at \( (2, -3) \).

   - **Domain:** As discussed, the domain for any quadratic function is all real numbers.
     \[
     \text{Domain}: (-\infty, \infty)
     \]
   - **Range:** Since the parabola opens upwards and the vertex is at \( (2, -3) \), the lowest point on the graph is \( -

Learn how to find the domain and range of quadratic functions with a detailed step-by-step guide. Understand the concepts behind quadratic functions, domain, and range. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation