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Graph f(x)=x². Compare the graph of y = f(x) to the graph of y=x². Use the graphing tool to graph the function. Click to enlarge graph Compare the graph of y = f(x) to the graph of y=x². Choose the correct answer below. O A. Both graphs are parabolas opening in the same direction, but the graph of y = f(x) is narrower than the graph of y=x². B. Both graphs are parabolas, but the graph of y = f(x) opens downward and is wider than the graph of y = x². (...) -20 16 12 -8 -4

Graph f(x)=x². Compare the graph of y = f(x) to the graph of y=x². Use the graphing tool to graph the function. Click to enlarge graph Compare the graph of y = f(x) to the graph of y=x². Choose the correct answer below. O A. Both graphs are parabolas opening in the same direction, but the graph of y = f(x) is narrower than the graph of y=x². B. Both graphs are parabolas, but the graph of y = f(x) opens downward and is wider than the graph of y = x². (...) -20 16 12 -8 -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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### Understanding Parabolas: Graph Comparison #### Graph Characteristics of Quadratic Functions When comparing the graphs of two quadratic functions, it's important to understand their orientation and shape. Here are two statements that describe differences between two such graphs. #### Option C: - **Statement**: Both graphs are parabolas, but the graph of \(y = f(x)\) opens downward and is narrower than the graph of \(y = x^2\). - **Explanation**: This describes two parabolic graphs where one (graph of \(y = f(x)\)) is inverted (opening downward) and appears more "compressed" or "narrower" than the standard upward-opening parabola \(y = x^2\). #### Option D: - **Statement**: Both graphs are parabolas opening in the same direction, but the graph of \(y = f(x)\) is wider than the graph of \(y = x^2\). - **Explanation**: Here, both parabolas open in the same (upward) direction, but the graph of \(y = f(x)\) is "stretched" or "wider" compared to the graph of \(y = x^2\). Understanding these descriptions helps in analyzing how transformations affect the shape and orientation of quadratic graphs.
Transcribed Image Text:### Understanding Parabolas: Graph Comparison #### Graph Characteristics of Quadratic Functions When comparing the graphs of two quadratic functions, it's important to understand their orientation and shape. Here are two statements that describe differences between two such graphs. #### Option C: - **Statement**: Both graphs are parabolas, but the graph of \(y = f(x)\) opens downward and is narrower than the graph of \(y = x^2\). - **Explanation**: This describes two parabolic graphs where one (graph of \(y = f(x)\)) is inverted (opening downward) and appears more "compressed" or "narrower" than the standard upward-opening parabola \(y = x^2\). #### Option D: - **Statement**: Both graphs are parabolas opening in the same direction, but the graph of \(y = f(x)\) is wider than the graph of \(y = x^2\). - **Explanation**: Here, both parabolas open in the same (upward) direction, but the graph of \(y = f(x)\) is "stretched" or "wider" compared to the graph of \(y = x^2\). Understanding these descriptions helps in analyzing how transformations affect the shape and orientation of quadratic graphs.
**Educational Content Transcription** --- ### Comparing Graphs of Quadratic Functions **Graph \( f(x) = \frac{1}{2}x^2 \). Compare the graph of \( y = f(x) \) to the graph of \( y = x^2 \).** **Use the graphing tool to graph the function.** [Click to enlarge graph] **Compare the graph of \( y = f(x) \) to the graph of \( y = x^2 \). Choose the correct answer below.** **A.** Both graphs are parabolas opening in the same direction, but the graph of \( y = f(x) \) is narrower than the graph of \( y = x^2 \). **B.** Both graphs are parabolas, but the graph of \( y = f(x) \) opens downward and is wider than the graph of \( y = x^2 \). --- **Graph Explanation:** There is a grid given on a coordinate plane. The x-axis and y-axis are marked from -20 to 20, with intervals of 4 marked and labeled. Both axes originate from the center point (0,0). The grid is extensive, spanning across all four quadrants. For a visual graphing: 1. **Graph of \( y = x^2 \):** - It is a standard parabola opening upwards. - The vertex is at the origin (0,0). - The parabola gets wider as it moves away from the vertex. 2. **Graph of \( y = \frac{1}{2}x^2 \):** - It is also a parabola opening upwards. - The vertex is at the origin (0,0). - This parabola is wider compared to the graph of \( y = x^2 \). **Correct Answer Discussion:** The graph of the function \( y = \frac{1}{2}x^2 \) is a wider parabola compared to the graph of \( y = x^2 \). Therefore, the graph of \( y = f(x) \) opens in the same direction (upward) but is wider than the graph of \( y = x^2 \). **The correct answer is:** B. Both graphs are parabolas, but the graph of \( y = f(x) \) opens downward and is wider than the graph of \( y
Transcribed Image Text:**Educational Content Transcription** --- ### Comparing Graphs of Quadratic Functions **Graph \( f(x) = \frac{1}{2}x^2 \). Compare the graph of \( y = f(x) \) to the graph of \( y = x^2 \).** **Use the graphing tool to graph the function.** [Click to enlarge graph] **Compare the graph of \( y = f(x) \) to the graph of \( y = x^2 \). Choose the correct answer below.** **A.** Both graphs are parabolas opening in the same direction, but the graph of \( y = f(x) \) is narrower than the graph of \( y = x^2 \). **B.** Both graphs are parabolas, but the graph of \( y = f(x) \) opens downward and is wider than the graph of \( y = x^2 \). --- **Graph Explanation:** There is a grid given on a coordinate plane. The x-axis and y-axis are marked from -20 to 20, with intervals of 4 marked and labeled. Both axes originate from the center point (0,0). The grid is extensive, spanning across all four quadrants. For a visual graphing: 1. **Graph of \( y = x^2 \):** - It is a standard parabola opening upwards. - The vertex is at the origin (0,0). - The parabola gets wider as it moves away from the vertex. 2. **Graph of \( y = \frac{1}{2}x^2 \):** - It is also a parabola opening upwards. - The vertex is at the origin (0,0). - This parabola is wider compared to the graph of \( y = x^2 \). **Correct Answer Discussion:** The graph of the function \( y = \frac{1}{2}x^2 \) is a wider parabola compared to the graph of \( y = x^2 \). Therefore, the graph of \( y = f(x) \) opens in the same direction (upward) but is wider than the graph of \( y = x^2 \). **The correct answer is:** B. Both graphs are parabolas, but the graph of \( y = f(x) \) opens downward and is wider than the graph of \( y
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