PER 2. y=2(x+4) -8 Vertex: 10 Axis of Symmetry: 8- Graph using the graphing pattern: 3- 109-8-7-6-5-4-3-2-1 2345 -2 3- 4 -5 Does graph open up or down?: -7 -8 Is the vertex a max or a min?: Domain: Range: O90 654 m N
PER 2. y=2(x+4) -8 Vertex: 10 Axis of Symmetry: 8- Graph using the graphing pattern: 3- 109-8-7-6-5-4-3-2-1 2345 -2 3- 4 -5 Does graph open up or down?: -7 -8 Is the vertex a max or a min?: Domain: Range: O90 654 m N
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Quadratic Function Exploration
**Equation:**
\[ y = 2(x+4)^2 - 8 \]
**Instructions:**
1. **Identify the Vertex:**
- The vertex of the parabola is the turning point of the graph. Use the equation to find this point.
2. **Determine the Axis of Symmetry:**
- The axis of symmetry is a vertical line that passes through the vertex.
3. **Graphing:**
- Utilize the grid to sketch the parabola according to the given equation. Pay attention to how the graph shifts or stretches compared to the standard form.
4. **Graph Characteristics:**
- **Direction:** Does the parabola open upwards or downwards?
- **Vertex Type:** Is the vertex a maximum or a minimum point?
- **Domain:** Describe the set of all possible x-values for the function.
- **Range:** Describe the set of all possible y-values for the function.
5. **Transformations:**
- Identify how the graph is transformed from the parent function \( y = x^2 \).
**Graph Description:**
The graph is a coordinate plane with labels ranging from -10 to 10 on both the x-axis and y-axis. Each axis is labeled with tic marks to help pinpoint specific coordinates. Use this grid to accurately plot the quadratic function as discussed above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73660c80-f4a9-47a1-984c-ecff297c0e62%2F4ecc2c3a-daf5-45d4-a185-77ddf9ebbafb%2Fi64kksui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Function Exploration
**Equation:**
\[ y = 2(x+4)^2 - 8 \]
**Instructions:**
1. **Identify the Vertex:**
- The vertex of the parabola is the turning point of the graph. Use the equation to find this point.
2. **Determine the Axis of Symmetry:**
- The axis of symmetry is a vertical line that passes through the vertex.
3. **Graphing:**
- Utilize the grid to sketch the parabola according to the given equation. Pay attention to how the graph shifts or stretches compared to the standard form.
4. **Graph Characteristics:**
- **Direction:** Does the parabola open upwards or downwards?
- **Vertex Type:** Is the vertex a maximum or a minimum point?
- **Domain:** Describe the set of all possible x-values for the function.
- **Range:** Describe the set of all possible y-values for the function.
5. **Transformations:**
- Identify how the graph is transformed from the parent function \( y = x^2 \).
**Graph Description:**
The graph is a coordinate plane with labels ranging from -10 to 10 on both the x-axis and y-axis. Each axis is labeled with tic marks to help pinpoint specific coordinates. Use this grid to accurately plot the quadratic function as discussed above.
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