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Graph f(x) = 4(x +4)² + 4.

Graph f(x) = 4(x +4)² + 4.

Algebra and Trigonometry (6th Edition)
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 the Function \( f(x) = 4(x + 4)^2 + 4 \) #### Description: The provided graph is a coordinate grid ranging from -10 to 10 on both the x and y axes. The graph displays the quadratic function \( f(x) = 4(x + 4)^2 + 4 \). #### Key Features: 1. **Quadratic Function**: This equation represents a parabola opening upwards. 2. **Vertex**: The vertex of the parabola is located at the point (-4, 4), determined by the transformation \( (x + 4) \). 3. **Axis of Symmetry**: The axis of symmetry is the vertical line \( x = -4 \). 4. **Stretch Factor**: The coefficient 4 indicates that the parabola is stretched vertically compared to the basic parabola \( y = x^2 \). 5. **Transformation**: There is a horizontal shift 4 units to the left and a vertical shift 4 units up from the origin. #### Visual Elements: - **Drawing Tools**: At the bottom, there are options to clear and draw lines, parabolas, check marks, circles, and dots on the graph. These tools can be used to explore different graphical representations. This graph provides a visual understanding of how transformations alter the standard parabola \( y = x^2 \) through horizontal and vertical shifts and vertical stretching.
Transcribed Image Text:### Graph of the Function \( f(x) = 4(x + 4)^2 + 4 \) #### Description: The provided graph is a coordinate grid ranging from -10 to 10 on both the x and y axes. The graph displays the quadratic function \( f(x) = 4(x + 4)^2 + 4 \). #### Key Features: 1. **Quadratic Function**: This equation represents a parabola opening upwards. 2. **Vertex**: The vertex of the parabola is located at the point (-4, 4), determined by the transformation \( (x + 4) \). 3. **Axis of Symmetry**: The axis of symmetry is the vertical line \( x = -4 \). 4. **Stretch Factor**: The coefficient 4 indicates that the parabola is stretched vertically compared to the basic parabola \( y = x^2 \). 5. **Transformation**: There is a horizontal shift 4 units to the left and a vertical shift 4 units up from the origin. #### Visual Elements: - **Drawing Tools**: At the bottom, there are options to clear and draw lines, parabolas, check marks, circles, and dots on the graph. These tools can be used to explore different graphical representations. This graph provides a visual understanding of how transformations alter the standard parabola \( y = x^2 \) through horizontal and vertical shifts and vertical stretching.
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