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O -8 -6-4 4 8 6 4 2 y 2 02 4 6 4 6

O -8 -6-4 4 8 6 4 2 y 2 02 4 6 4 6

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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### Graph Analysis and Transcription The images depict two separate graphs of quadratic functions on a coordinate plane. #### Graph 1: - **Axes**: The x-axis and y-axis intersect at the origin (0,0). - **Quadratic Curve**: The vertex of the parabola is located at the point (2, 0), suggesting the parabola opens upwards. - **Domain and Range**: The parabola extends indefinitely in the x-direction, with its lowest point at y = 0, moving upwards beyond y = 8. - **Symmetry**: The graph is symmetrical about the vertical line passing through x = 2. #### Graph 2: - **Axes**: The x-axis and y-axis intersect at the origin (0,0). - **Quadratic Curve**: The vertex of the parabola is at approximately the point (-4, 0), indicating this parabola opens upwards. - **Domain and Range**: The parabola extends indefinitely in the x-direction with its lowest point at y = 0, and it increases beyond y = 8. - **Symmetry**: The graph is symmetrical about the vertical line passing through x = -4. ### Educational Note Both graphs represent quadratic functions in the vertex form \( y = a(x-h)^2 + k \), where \((h, k)\) is the vertex. They illustrate the impact of the horizontal translation on parabola orientation and position.
Transcribed Image Text:### Graph Analysis and Transcription The images depict two separate graphs of quadratic functions on a coordinate plane. #### Graph 1: - **Axes**: The x-axis and y-axis intersect at the origin (0,0). - **Quadratic Curve**: The vertex of the parabola is located at the point (2, 0), suggesting the parabola opens upwards. - **Domain and Range**: The parabola extends indefinitely in the x-direction, with its lowest point at y = 0, moving upwards beyond y = 8. - **Symmetry**: The graph is symmetrical about the vertical line passing through x = 2. #### Graph 2: - **Axes**: The x-axis and y-axis intersect at the origin (0,0). - **Quadratic Curve**: The vertex of the parabola is at approximately the point (-4, 0), indicating this parabola opens upwards. - **Domain and Range**: The parabola extends indefinitely in the x-direction with its lowest point at y = 0, and it increases beyond y = 8. - **Symmetry**: The graph is symmetrical about the vertical line passing through x = -4. ### Educational Note Both graphs represent quadratic functions in the vertex form \( y = a(x-h)^2 + k \), where \((h, k)\) is the vertex. They illustrate the impact of the horizontal translation on parabola orientation and position.
### Question 20: Identifying a Parabola with a Minimum Vertex **Question**: Which graph shows a parabola with a vertex at \((-3, 2)\) that is a minimum value? #### Graph Analysis **Top Graph:** - **Vertex**: Located at \((-3, 5)\). - The parabola opens downward, indicating a maximum value at its vertex. **Bottom Graph:** - **Vertex**: Located at \((-3, 2)\). - The parabola opens upward, indicating a minimum value at its vertex. #### Conclusion The bottom graph shows a parabola with a vertex at \((-3, 2)\) that is a minimum value.
Transcribed Image Text:### Question 20: Identifying a Parabola with a Minimum Vertex **Question**: Which graph shows a parabola with a vertex at \((-3, 2)\) that is a minimum value? #### Graph Analysis **Top Graph:** - **Vertex**: Located at \((-3, 5)\). - The parabola opens downward, indicating a maximum value at its vertex. **Bottom Graph:** - **Vertex**: Located at \((-3, 2)\). - The parabola opens upward, indicating a minimum value at its vertex. #### Conclusion The bottom graph shows a parabola with a vertex at \((-3, 2)\) that is a minimum value.
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