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Order the group of quadratic functions from widest to narrowest graph y = 3x² y = x² y = 2x² I

Order the group of quadratic functions from widest to narrowest graph y = 3x² y = x² y = 2x² I

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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**Title:** Ordering Quadratic Functions by Graph Width **Instructions:** Order the group of quadratic functions from the widest to the narrowest graph. **Quadratic Functions:** 1. \( y = 3x^2 \) 2. \( y = x^2 \) 3. \( y = 2x^2 \) **Options:** - **a**: \( y = 3x^2 \), \( y = 2x^2 \), \( y = x^2 \) - **b**: \( y = 2x^2 \), \( y = x^2 \), \( y = 3x^2 \) - **c**: \( y = x^2 \), \( y = 2x^2 \), \( y = 3x^2 \) - **d**: \( y = x^2 \), \( y = 3x^2 \), \( y = 2x^2 \) **Explanation:** Each function represents a parabola, and the coefficient before \( x^2 \) determines the width of the parabola. The smaller the coefficient, the wider the graph appears. Therefore, in option **c**, the functions are correctly ordered from the widest to the narrowest: \( y = x^2 \), \( y = 2x^2 \), \( y = 3x^2 \).
Transcribed Image Text:**Title:** Ordering Quadratic Functions by Graph Width **Instructions:** Order the group of quadratic functions from the widest to the narrowest graph. **Quadratic Functions:** 1. \( y = 3x^2 \) 2. \( y = x^2 \) 3. \( y = 2x^2 \) **Options:** - **a**: \( y = 3x^2 \), \( y = 2x^2 \), \( y = x^2 \) - **b**: \( y = 2x^2 \), \( y = x^2 \), \( y = 3x^2 \) - **c**: \( y = x^2 \), \( y = 2x^2 \), \( y = 3x^2 \) - **d**: \( y = x^2 \), \( y = 3x^2 \), \( y = 2x^2 \) **Explanation:** Each function represents a parabola, and the coefficient before \( x^2 \) determines the width of the parabola. The smaller the coefficient, the wider the graph appears. Therefore, in option **c**, the functions are correctly ordered from the widest to the narrowest: \( y = x^2 \), \( y = 2x^2 \), \( y = 3x^2 \).
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