Determine its image point after the transformation

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Discussion Overview

The discussion revolves around the transformation of the graph of the function y=x^2 to the function y=-3(x+5)-2, specifically focusing on determining the image point of the point (-3, 9) after the transformation. The scope includes mathematical reasoning and clarification of the transformation process.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents the transformation rule for points on the graph of y=x^2 to a vertex form of a quadratic equation, suggesting a mapping rule of (x,y) → (x+h, ay+k).
  • Another participant questions the interpretation of the transformation, suggesting that the correct function might be y=-3(x+5)^2-2 rather than y=-3(x+5)-2, indicating a potential misunderstanding in the notation.
  • A participant calculates the transformed image point of (-3, 9) as (2, -29) based on the assumption that the transformation is correctly interpreted as y=-3(x+5)^2-2.
  • There is a request for clarification regarding the notation used in the transformation, specifically whether the exponent was omitted or if there was a typographical error.

Areas of Agreement / Disagreement

Participants express uncertainty about the correct interpretation of the transformation notation, leading to multiple competing views regarding the proper form of the function and the resulting image point. The discussion remains unresolved as participants seek clarification.

Contextual Notes

There are limitations regarding the clarity of the transformation notation, which affects the understanding of the transformation process. The discussion also highlights the dependence on the correct interpretation of the function's form.

Azurin
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The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2. The point (-3, 9) lies on the graph of y=x^2. Determine its image point after the transformations.
 
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Azurin said:
Azurin said:
The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2. The point (-3, 9) lies on the graph of y=x^2. Determine its image point after the transformations.
Skeeter is assuming the function is [math]y= -3(x+5)^2- 2[/math], not [math]y= -3(x+5) 2[/math].
Is that correct?

If so, I would observe that x has 5 added to it and that y (everything done after the squaring) is multiplied by -3 then had 2 subtracted. that is, (x, y) is transformed to (x+ 5, -3y- 2). In particular (-3, 9) is transformed to (-3+ 5, -3(9)- 2)= (2, -29).

Check- yes, if x= 2, [math]y= -3(-2+ 5)^2- 2= -3(3)^2- 2= -27- 2= -29[/math].
 
Last edited:
You wrote
The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2.

Did you mean "y= -3(x+ 5)^2- 2" or just "y= -3(x+ 5)^2"? In other words, did you drop the "^" or did you type "-" instead of "^"?
 

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