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Which of the following is the graph of (y-2)² = −4(x - 2)² 12 5 n 24 X + 3 24 CV 9 T ny 7 T O & 7 6 7 7 & 9 T ❤ 14 D A ✔ N 7 24 17 + O 4 20 2₂ 6 T T 9 4

Which of the following is the graph of (y-2)² = −4(x - 2)² 12 5 n 24 X + 3 24 CV 9 T ny 7 T O & 7 6 7 7 & 9 T ❤ 14 D A ✔ N 7 24 17 + O 4 20 2₂ 6 T T 9 4

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question:** Which of the following is the graph of \((y - 2)^2 = -4(x - 2)\)? **Graph Descriptions:** 1. **First Graph:** - The graph shows a parabola opening to the left. - The vertex of the parabola is at the point (2, 2). - The y-axis ranges approximately from -10 to 10. - The x-axis ranges approximately from -10 to 10. 2. **Second Graph:** - The graph shows a parabola opening to the left. - The vertex of the parabola is at the point (2, 2). - The y-axis ranges approximately from -10 to 10. - The x-axis ranges approximately from -10 to 10. Both graphs depict parabolas opening to the left with the vertex at the same point, which is consistent with the equation \((y - 2)^2 = -4(x - 2)\). However, the context or details provided in the original question should be used to select the correct graph if they are meant to represent different options or simply duplicated for some educational purpose.
Transcribed Image Text:**Question:** Which of the following is the graph of \((y - 2)^2 = -4(x - 2)\)? **Graph Descriptions:** 1. **First Graph:** - The graph shows a parabola opening to the left. - The vertex of the parabola is at the point (2, 2). - The y-axis ranges approximately from -10 to 10. - The x-axis ranges approximately from -10 to 10. 2. **Second Graph:** - The graph shows a parabola opening to the left. - The vertex of the parabola is at the point (2, 2). - The y-axis ranges approximately from -10 to 10. - The x-axis ranges approximately from -10 to 10. Both graphs depict parabolas opening to the left with the vertex at the same point, which is consistent with the equation \((y - 2)^2 = -4(x - 2)\). However, the context or details provided in the original question should be used to select the correct graph if they are meant to represent different options or simply duplicated for some educational purpose.
### Exploring Quadratic Functions #### Introduction to Quadratic Graphs Quadratic functions are polynomial functions of the form \( f(x) = ax^2 + bx + c \). These functions create parabolic graphs, which can either open upwards or downwards depending on the coefficient \( a \). #### Graphs of Quadratic Functions Below are two examples of quadratic function graphs, showcasing different orientations and vertex positions. #### Figure 1: Upwards Opening Parabola ![Graph 1](image_link) **Description:** This graph illustrates a quadratic function with the equation \( y = x^2 - 2x + 1 \), resulting in a parabola that opens upwards. The key features of this graph include: - **Vertex:** The lowest point on the graph is at (1, -3). - **Axis of Symmetry:** The vertical line that passes through the vertex, \( x = 1 \). - **X-intercepts (Roots):** The points where the graph crosses the x-axis, approximately at \( x = -1 \) and \( x = 3 \). - **Y-intercept:** The point where the graph crosses the y-axis, at \( y = 1 \). #### Figure 2: Downwards Opening Parabola ![Graph 2](image_link) **Description:** This graph demonstrates a quadratic function with the equation \( y = -x^2 + 4x - 3 \), leading to a parabola that opens downwards. The notable features include: - **Vertex:** The highest point on the graph is at (2, 1). - **Axis of Symmetry:** The vertical line that passes through the vertex, \( x = 2 \). - **X-intercepts (Roots):** The points where the graph crosses the x-axis, approximately at \( x = 1 \) and \( x = 3 \). - **Y-intercept:** The point where the graph crosses the y-axis, at \( y = -3 \). #### Conclusion In summary, the orientation of a parabolic graph is determined by the coefficient \( a \) in the quadratic equation \( y = ax^2 + bx + c \). If \( a > 0 \), the parabola opens upwards, and if \( a < 0 \), it opens downwards. Understanding these properties is fundamental in analyzing quadratic functions. For further investigation, students can change the coefficients
Transcribed Image Text:### Exploring Quadratic Functions #### Introduction to Quadratic Graphs Quadratic functions are polynomial functions of the form \( f(x) = ax^2 + bx + c \). These functions create parabolic graphs, which can either open upwards or downwards depending on the coefficient \( a \). #### Graphs of Quadratic Functions Below are two examples of quadratic function graphs, showcasing different orientations and vertex positions. #### Figure 1: Upwards Opening Parabola ![Graph 1](image_link) **Description:** This graph illustrates a quadratic function with the equation \( y = x^2 - 2x + 1 \), resulting in a parabola that opens upwards. The key features of this graph include: - **Vertex:** The lowest point on the graph is at (1, -3). - **Axis of Symmetry:** The vertical line that passes through the vertex, \( x = 1 \). - **X-intercepts (Roots):** The points where the graph crosses the x-axis, approximately at \( x = -1 \) and \( x = 3 \). - **Y-intercept:** The point where the graph crosses the y-axis, at \( y = 1 \). #### Figure 2: Downwards Opening Parabola ![Graph 2](image_link) **Description:** This graph demonstrates a quadratic function with the equation \( y = -x^2 + 4x - 3 \), leading to a parabola that opens downwards. The notable features include: - **Vertex:** The highest point on the graph is at (2, 1). - **Axis of Symmetry:** The vertical line that passes through the vertex, \( x = 2 \). - **X-intercepts (Roots):** The points where the graph crosses the x-axis, approximately at \( x = 1 \) and \( x = 3 \). - **Y-intercept:** The point where the graph crosses the y-axis, at \( y = -3 \). #### Conclusion In summary, the orientation of a parabolic graph is determined by the coefficient \( a \) in the quadratic equation \( y = ax^2 + bx + c \). If \( a > 0 \), the parabola opens upwards, and if \( a < 0 \), it opens downwards. Understanding these properties is fundamental in analyzing quadratic functions. For further investigation, students can change the coefficients
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