Graph the following quadratic function using its properties. Based on the graph, determine the domain and range of the quadratic function. f(x)=x² - 6x + 5 www
Graph the following quadratic function using its properties. Based on the graph, determine the domain and range of the quadratic function. f(x)=x² - 6x + 5 www
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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![**Graphing Quadratic Functions: An Instructional Guide**
### Task:
Graph the following quadratic function using its properties. Based on the graph, determine the domain and range of the quadratic function.
\[ f(x) = x^2 - 6x + 5 \]
---
#### Instructions:
1. **Use the Graphing Tool**
- Click the button labeled "Click to enlarge graph" to access the graphing tool and begin plotting the function.
2. **Graph Details**
- The quadratic function \( f(x) = x^2 - 6x + 5 \) is a parabola.
- You can identify the vertex, axis of symmetry, and the direction in which the parabola opens by expanding and converting the function into vertex form if necessary.
3. **Determine Domain and Range**
- **Domain**: The domain of any quadratic function is all real numbers, \(-\infty, \infty\).
- **Range**: Based on the vertex of the graph and the direction in which the parabola opens (upward if the coefficient of \( x^2 \) is positive), the range will vary.
#### Graph Explanation:
- **Graph Axes**
- X-axis: Horizontal line indicating the values of \( x \).
- Y-axis: Vertical line indicating the values of \( f(x) \).
- **Plotting the Function**
- Identify the vertex by completing the square or using the formula \( x = \frac{-b}{2a} \) for the vertex \( x\)-coordinate.
- Once the vertex is plotted, choose additional points on either side of the vertex to plot the symmetrical nature of the parabola.
### Interactive Tip:
Use the interactive graphing tool to adjust and visualize the parabola on the graph grid. Ensure that the plot properly extends to illustrate the key features: vertex, axis of symmetry, x-intercepts, and y-intercept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5feb7218-6da5-48e9-9bc9-7d0ced0f9782%2F203a217d-c014-4e07-b1f4-267ab7651b8f%2Fuhwfgd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing Quadratic Functions: An Instructional Guide**
### Task:
Graph the following quadratic function using its properties. Based on the graph, determine the domain and range of the quadratic function.
\[ f(x) = x^2 - 6x + 5 \]
---
#### Instructions:
1. **Use the Graphing Tool**
- Click the button labeled "Click to enlarge graph" to access the graphing tool and begin plotting the function.
2. **Graph Details**
- The quadratic function \( f(x) = x^2 - 6x + 5 \) is a parabola.
- You can identify the vertex, axis of symmetry, and the direction in which the parabola opens by expanding and converting the function into vertex form if necessary.
3. **Determine Domain and Range**
- **Domain**: The domain of any quadratic function is all real numbers, \(-\infty, \infty\).
- **Range**: Based on the vertex of the graph and the direction in which the parabola opens (upward if the coefficient of \( x^2 \) is positive), the range will vary.
#### Graph Explanation:
- **Graph Axes**
- X-axis: Horizontal line indicating the values of \( x \).
- Y-axis: Vertical line indicating the values of \( f(x) \).
- **Plotting the Function**
- Identify the vertex by completing the square or using the formula \( x = \frac{-b}{2a} \) for the vertex \( x\)-coordinate.
- Once the vertex is plotted, choose additional points on either side of the vertex to plot the symmetrical nature of the parabola.
### Interactive Tip:
Use the interactive graphing tool to adjust and visualize the parabola on the graph grid. Ensure that the plot properly extends to illustrate the key features: vertex, axis of symmetry, x-intercepts, and y-intercept.
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