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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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.

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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