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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Question
![### Graph of Absolute Value Function:
**Objective:**
Write the equation for the graph shown below in the form \( y = a |x - h| + k \). The point is marking the vertex of the graph.
**Graph Description:**
The graph shows a V-shaped curve, typical of an absolute value function. The vertex of the graph is marked on a Cartesian coordinate system.
**Graph Explanation:**
1. **Axes:**
- The x-axis ranges from -10 to 10.
- The y-axis ranges from -10 to 10.
2. **Vertex:**
- The vertex of the graph is located at the point (-1, -4). This represents the point (h, k) in the equation \( y = a |x - h| + k \).
3. **Lines:**
- The V-shape indicates that the graph of the absolute value function opens upwards.
- At \( x = -1 \), the lowest point on the graph is at \( y = -4 \).
**Determining the 'a' Value:**
To determine the value of 'a', choose another point on the graph to identify the slope. For instance:
- When \( x = 0 \), \( y = -5 \).
Using the vertex form equation:
\[ y = a|x + 1| - 4 \]
Substituting the point (0, -5):
\[ -5 = a|0 + 1| - 4 \]
\[ -5 = a \cdot 1 - 4 \]
\[ -5 + 4 = a \]
\[ a = -1 \]
### Conclusion:
Therefore, the equation for the graph is:
\[ y = -1 |x + 1| - 4 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6691cd2-55cd-462f-8290-5296a9107f11%2F3adb9aec-38f9-4546-b2df-e81b96bfb064%2F44bzr7u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graph of Absolute Value Function:
**Objective:**
Write the equation for the graph shown below in the form \( y = a |x - h| + k \). The point is marking the vertex of the graph.
**Graph Description:**
The graph shows a V-shaped curve, typical of an absolute value function. The vertex of the graph is marked on a Cartesian coordinate system.
**Graph Explanation:**
1. **Axes:**
- The x-axis ranges from -10 to 10.
- The y-axis ranges from -10 to 10.
2. **Vertex:**
- The vertex of the graph is located at the point (-1, -4). This represents the point (h, k) in the equation \( y = a |x - h| + k \).
3. **Lines:**
- The V-shape indicates that the graph of the absolute value function opens upwards.
- At \( x = -1 \), the lowest point on the graph is at \( y = -4 \).
**Determining the 'a' Value:**
To determine the value of 'a', choose another point on the graph to identify the slope. For instance:
- When \( x = 0 \), \( y = -5 \).
Using the vertex form equation:
\[ y = a|x + 1| - 4 \]
Substituting the point (0, -5):
\[ -5 = a|0 + 1| - 4 \]
\[ -5 = a \cdot 1 - 4 \]
\[ -5 + 4 = a \]
\[ a = -1 \]
### Conclusion:
Therefore, the equation for the graph is:
\[ y = -1 |x + 1| - 4 \]
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