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Question 13. A quadratic function is a function p: RR which can be written in the form p(x) = ax² + bx+c, where a, b, c ER and a # 0. Demonstrate that every quadratic function can be understood as a transformation (translated, scaled, and possibly reflected) of the primitive quadratic function q: R→R:xx².

Question 13. A quadratic function is a function p: RR which can be written in the form p(x) = ax² + bx+c, where a, b, c ER and a # 0. Demonstrate that every quadratic function can be understood as a transformation (translated, scaled, and possibly reflected) of the primitive quadratic function q: R→R:xx².

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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W6 Question 13

Question 13. A quadratic function is a function p: RR which can be written in the form p(x) = ax² + bx + c₂ where a, b, c ≤ R and a # 0. Demonstrate that every quadratic function can be understood as a transformation (translated, scaled, and possibly reflected) of the primitive quadratic function q : R → R : x →x². To address this question, consider what these geometric transformations will do to the formula which defines q, and compare that to the formula which defines p. Turn in this problem. Explain the process which gets you to an answer, and keep in mind that your grammar, spelling, and style are important. Do your scratch work separately, and write up a “final draft” to turn in.
Transcribed Image Text:Question 13. A quadratic function is a function p: RR which can be written in the form p(x) = ax² + bx + c₂ where a, b, c ≤ R and a # 0. Demonstrate that every quadratic function can be understood as a transformation (translated, scaled, and possibly reflected) of the primitive quadratic function q : R → R : x →x². To address this question, consider what these geometric transformations will do to the formula which defines q, and compare that to the formula which defines p. Turn in this problem. Explain the process which gets you to an answer, and keep in mind that your grammar, spelling, and style are important. Do your scratch work separately, and write up a “final draft” to turn in.
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