The graph of a quadratic function with vertex (0, -2) is shown in the figure below. Find the range and the domain. Write the range and domain using interval notation.
The graph of a quadratic function with vertex (0, -2) is shown in the figure below. Find the range and the domain. Write the range and domain using interval notation.
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 a quadratic function with vertex (0, -2) is shown in the figure below.
Find the range and the domain. Write the range and domain using interval notation.
The graph displays a parabola that opens downwards with its vertex at the point \((0, -2)\). The x-axis ranges from \(-10\) to \(10\) and the y-axis ranges from \(-10\) to \(10\).
**Explanation:**
- The parabolic curve indicates that the function is a downward-opening quadratic.
- The vertex is the highest point on the graph, meaning the maximum value of the function is at \(y = -2\).
**Domain and Range in Interval Notation:**
(a) **Range:**
- The range consists of all \(y\)-values that the graph attains. Since the parabola opens downward, the maximum \(y\)-value is \(-2\) and it decreases indefinitely.
- **Range:** \((-\infty, -2]\)
(b) **Domain:**
- The domain consists of all possible \(x\)-values the function can take. For a quadratic function, the graph extends infinitely in both directions along the x-axis.
- **Domain:** \((-\infty, \infty)\)
**Interval Notation Selection:**
- Options are displayed in boxes: \((-\infty, \infty)\), \([0, 0]\), \((0, 0]\), etc.
- The correct selections for this function are for range \((-\infty, -2]\) and for domain \((-\infty, \infty)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5aa4bbb4-d01e-4d70-a118-60f9a7365aeb%2F8a584eb5-79f1-4c40-91ee-77cb451ab85a%2Fjqt5i1v_processed.png&w=3840&q=75)
Transcribed Image Text:**Polynomial and Rational Functions**
**Domain and Range from the Graph of a Quadratic Function**
The graph of a quadratic function with vertex \((0, -2)\) is shown in the figure below. Find the range and the domain.
The graph displays a parabola that opens downwards with its vertex at the point \((0, -2)\). The x-axis ranges from \(-10\) to \(10\) and the y-axis ranges from \(-10\) to \(10\).
**Explanation:**
- The parabolic curve indicates that the function is a downward-opening quadratic.
- The vertex is the highest point on the graph, meaning the maximum value of the function is at \(y = -2\).
**Domain and Range in Interval Notation:**
(a) **Range:**
- The range consists of all \(y\)-values that the graph attains. Since the parabola opens downward, the maximum \(y\)-value is \(-2\) and it decreases indefinitely.
- **Range:** \((-\infty, -2]\)
(b) **Domain:**
- The domain consists of all possible \(x\)-values the function can take. For a quadratic function, the graph extends infinitely in both directions along the x-axis.
- **Domain:** \((-\infty, \infty)\)
**Interval Notation Selection:**
- Options are displayed in boxes: \((-\infty, \infty)\), \([0, 0]\), \((0, 0]\), etc.
- The correct selections for this function are for range \((-\infty, -2]\) and for domain \((-\infty, \infty)\).
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