Mathopolis: Transforming Function Qs

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SUMMARY

The discussion centers on the transformation of the function from the standard form X^2 + 2x + 4 to the vertex form (x + 4)^2 + 2(x + 4). Participants express confusion regarding the representation of the function and the appearance of multiple instances of (x + 4). The main focus is on understanding the conversion process and the reasoning behind the transformation, which is crucial for grasping function manipulation in algebra.

PREREQUISITES
  • Understanding of quadratic functions and their standard forms
  • Familiarity with function transformations, specifically vertex form
  • Basic algebraic manipulation skills
  • Knowledge of polynomial expressions and factoring techniques
NEXT STEPS
  • Study the process of converting quadratic functions to vertex form
  • Learn about completing the square in polynomial expressions
  • Explore the implications of function transformations on graph behavior
  • Practice problems involving quadratic equations and their transformations
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Students learning algebra, educators teaching quadratic functions, and anyone seeking to deepen their understanding of function transformations in mathematics.

caligari
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I was wondering why this function was this answer and not X^2+2x+4 and why it is in the form that it is. Is it just some rule that you put it in that form? In the answer given, (x + 4)2 + 2(x + 4) , I don't understand how you get 3 different (x+4). Even though the answer is right there and it explains it I still don't get it. X^2+2x+4 makes sense to me.
 
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Which question number are you talking about?

caligari said:
In the answer given, (x + 4)2 + 2(x + 4) , I don't understand how you get 3 different (x+4).
Where do you see three different $(x+4)$ in $(x + 4)^2 + 2(x + 4)$?

caligari said:
Even though the answer is right there and it explains it
What exactly explains it?
 

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