How can completing the square help with graphing transformations?

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Homework Help Overview

The discussion revolves around graphing the function f(x)=x^2+4x+3 by utilizing transformations of the basic quadratic function y=x^2. Participants are exploring the concept of completing the square to aid in understanding these transformations.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the transformation properties of functions and suggest converting the quadratic function into its completed square form to facilitate graphing. There are inquiries about the meaning of specific terms in the context of the graph.

Discussion Status

Some participants have provided guidance on completing the square as a method to clarify the transformations involved. There is an ongoing exploration of how to interpret the function's components in relation to its graph.

Contextual Notes

One participant expresses uncertainty about transformations and their application, indicating a need for further clarification on the topic. The original poster seeks assistance in understanding these concepts without providing a complete solution.

shoook
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1. Graph the function f(x)=x^2+4x+3 by starting with the graph of y=x^2 and using transformations.



2.



3. I know the graph opens up, but I don't understand transformations or how to solve them, any help would be greatly appreciated.
 
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For any function f(x), f(x-a) moves the graph right by a units, a*f(x) stretches the graph by a factor of "a", f(ax) increases the frequency of the graph "a" times, f(x)-a moves a graph down by "a" units.
 
Well to help you see better change f(x) into the completed square form
 
If you think physically (i.e. like a freefall problem), you can almost immediately pick out the meaning of the constant 3 term and the 4x term... then transform the original y=x^2 appropriately.
 
To repeat the very good advice of rock_freak667, complete the square- and it all shall be made clear to you!
 

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