MHB Mathopolis: Transforming Function Qs

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The discussion centers around confusion regarding the transformation of a function into a specific form, particularly the expression (x + 4)² + 2(x + 4). Participants seek clarification on the reasoning behind this transformation compared to the standard quadratic form x² + 2x + 4. There is a specific inquiry about the presence of three instances of (x + 4) in the expression, which leads to further questions about the explanation provided. The conversation highlights a need for clearer understanding of function transformations and their representations. Overall, the thread emphasizes the importance of comprehending mathematical rules and their applications.
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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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