Mastering Quartic & Quintic Graphing w/o a Calculator for Pre-Calc 12

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    Calculator Graphing
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Discussion Overview

The discussion revolves around the necessity for pre-calculus 12 students to master graphing quartic and quintic functions without the aid of a graphing calculator. It explores the implications of different forms of polynomial functions on the ability to graph them accurately.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • Some participants suggest that the need to master graphing quartic or quintic functions without a calculator depends on how the functions are presented, particularly whether they are in factored form.
  • Others argue that if the functions are not given in factored form, it may be difficult or impossible to determine exact x-intercepts for certain fifth-degree polynomials.
  • One participant questions the necessity of having a graphing calculator in class, sharing their personal experience of never needing one.
  • Another participant echoes this sentiment, suggesting that unless explicitly required by a teacher, a graphing calculator may not be necessary.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of mastering graphing without a calculator, with no consensus reached on the overall importance of graphing calculators in the classroom.

Contextual Notes

The discussion highlights the challenges associated with graphing higher-degree polynomials, particularly when not presented in a simplified form, but does not resolve the implications of these challenges.

Martin Zhao
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For pre-calculus 12, is there a need for students to master the ability of graphing quartic or quintic functions without using graphing calculator?
 
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Martin Zhao said:
For pre-calculus 12, is there a need for students to master the ability of graphing quartic or quintic functions without using graphing calculator?
I think it depends on how the functions are presented and how complicated they are. If they are given in factored form, then it's useful to be able to graph them. If they are not given in factored form it would be difficult or even impossible (in the case of some 5th degree polynomials) to find the exact values of the x-intercepts.
 
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For the senior high students, do you suggest them getting a graphing calculator in class?
 
Martin Zhao said:
For the senior high students, do you suggest them getting a graphing calculator in class?

I have never used a graphing calculator in my life and I never needed it. So unless your teacher specifically told you that you need one for class, I wouldn't bother.
 
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