Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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the graph of the quadratic function with vertex (1,4) is shown in the figure below, find the domain and range and write the domain and range using interval notation
![### Exploring the Domain and Range of Quadratic Functions
**Problem Statement:**
The graph of a quadratic function with vertex (1, 4) is shown in the figure below. Find the domain and the range.
**Graph Description:**
The graph depicted is a parabola opening upwards with its vertex at the point (1, 4).
**Visual Analysis of the Graph:**
- **X-axis range:** The graph extends infinitely in the x-direction.
- **Y-axis range:** The graph starts from the vertex at y = 4 and extends infinitely upwards.
**Question:**
"Write the domain and range using interval notation."
**Explanation of Interval Notation for This Graph:**
1. **Domain:**
- The domain of a quadratic function is all real numbers because, for any x-value, there is a corresponding y-value on the graph.
- In interval notation, this is expressed as:
\[
\text{Domain} = (-\infty, +\infty)
\]
2. **Range:**
- The range starts at the vertex's y-value and goes upwards. For this graph, the lowest y-value is 4.
- In interval notation, this is expressed as:
\[
\text{Range} = [4, +\infty)
\]
**Interactive Section:**
Included below is an input section where you can check your understanding by writing the domain and range using interval notation.
- **Domain:** [Dropdown options or input field]
- **Range:** [Dropdown options or input field]
Check your answers using the button below!
**Explanation Button:**
If you run into difficulties, press the "Explanation" button for a detailed step-by-step solution.
---
This educational content is designed to help you visualize and understand the domain and range of quadratic functions with an interactive approach.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47786e8c-2a51-4f4e-a0fc-479b515f394a%2F228e1d9c-a1cf-468d-98ab-4764477f1524%2F1pi5qg.jpeg&w=3840&q=75)
Transcribed Image Text:### Exploring the Domain and Range of Quadratic Functions
**Problem Statement:**
The graph of a quadratic function with vertex (1, 4) is shown in the figure below. Find the domain and the range.
**Graph Description:**
The graph depicted is a parabola opening upwards with its vertex at the point (1, 4).
**Visual Analysis of the Graph:**
- **X-axis range:** The graph extends infinitely in the x-direction.
- **Y-axis range:** The graph starts from the vertex at y = 4 and extends infinitely upwards.
**Question:**
"Write the domain and range using interval notation."
**Explanation of Interval Notation for This Graph:**
1. **Domain:**
- The domain of a quadratic function is all real numbers because, for any x-value, there is a corresponding y-value on the graph.
- In interval notation, this is expressed as:
\[
\text{Domain} = (-\infty, +\infty)
\]
2. **Range:**
- The range starts at the vertex's y-value and goes upwards. For this graph, the lowest y-value is 4.
- In interval notation, this is expressed as:
\[
\text{Range} = [4, +\infty)
\]
**Interactive Section:**
Included below is an input section where you can check your understanding by writing the domain and range using interval notation.
- **Domain:** [Dropdown options or input field]
- **Range:** [Dropdown options or input field]
Check your answers using the button below!
**Explanation Button:**
If you run into difficulties, press the "Explanation" button for a detailed step-by-step solution.
---
This educational content is designed to help you visualize and understand the domain and range of quadratic functions with an interactive approach.
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