The graph of a quadratic function with vertex (4, 2) is shown in the figure below. Find the range and the domain. 10- 4- 10 10 Write the range and domain using interval notation. (a) range: (0.0) (0.0) (00) [0.0) の DUD (b) domain: -00 8.
The graph of a quadratic function with vertex (4, 2) is shown in the figure below. Find the range and the domain. 10- 4- 10 10 Write the range and domain using interval notation. (a) range: (0.0) (0.0) (00) [0.0) の DUD (b) domain: -00 8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Domain and Range from the Graph of a Quadratic Function**
The graph of a quadratic function with vertex \( (4, 2) \) is shown in the figure below. Find the range and the domain.
### Graph Description:
- The graph is a parabola opening downwards.
- The vertex of the parabola is at the point \( (4, 2) \).
### Writing the Range and Domain Using Interval Notation:
**(a) Range**:
The range of the function is from \( -\infty \) to \( 2 \] because the parabola opens downwards and the maximum value is at the vertex.
**(b) Domain**:
The domain of the function is all real numbers, from \( -\infty \) to \( +\infty \), as the parabola extends infinitely in both directions horizontally.
### Options for Range and Domain:
1. Range: Select from the option \( -\infty, 2 \] \)
2. Domain: Choose \( -\infty, \infty \)
### Buttons:
- **Explanation**: Provides a detailed explanation of the solution.
- **Check**: To verify the answer.
This page is designed to help understand the domain and range of quadratic functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b823f6-a59b-43f1-924e-a48b4e93719a%2F5988d87e-02bd-4307-ab24-5bd0bb1b8635%2F4egnzqc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Domain and Range from the Graph of a Quadratic Function**
The graph of a quadratic function with vertex \( (4, 2) \) is shown in the figure below. Find the range and the domain.
### Graph Description:
- The graph is a parabola opening downwards.
- The vertex of the parabola is at the point \( (4, 2) \).
### Writing the Range and Domain Using Interval Notation:
**(a) Range**:
The range of the function is from \( -\infty \) to \( 2 \] because the parabola opens downwards and the maximum value is at the vertex.
**(b) Domain**:
The domain of the function is all real numbers, from \( -\infty \) to \( +\infty \), as the parabola extends infinitely in both directions horizontally.
### Options for Range and Domain:
1. Range: Select from the option \( -\infty, 2 \] \)
2. Domain: Choose \( -\infty, \infty \)
### Buttons:
- **Explanation**: Provides a detailed explanation of the solution.
- **Check**: To verify the answer.
This page is designed to help understand the domain and range of quadratic functions.
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