Rewriting f(x) as a Transformation of g(x)

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Homework Help Overview

The discussion revolves around rewriting the function f(x) in terms of transformations of the function g(x), specifically focusing on the vertex form of a quadratic equation. The subject area is algebra, particularly the manipulation of quadratic functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss completing the square to rewrite f(x) and express it in terms of transformations relative to g(x). There are questions about the correct formulation of the vertex form and the parameters h and k. Some participants seek clarification on how to interpret these transformations visually in relation to the graph of g(x).

Discussion Status

The discussion is active, with participants sharing their attempts at rewriting the function and questioning each other's formulations. There is a focus on ensuring the correct interpretation of the parameters involved in the transformation.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use. There is an emphasis on understanding the transformations without providing complete solutions.

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Homework Statement



Can someone assist me with number 3 please...

Homework Equations





The Attempt at a Solution



I went ahead and rewrote f(x) in vertex form in terms of a,b, and c but I'm having a hard time writing down how f can be thought of as a transformation of g.
 

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What did you get? You have f(x) = ax2 + bx + c. Complete the square to get this into a form so that you can recognize the translations and other transformations relative to the graph of y = x2.
 


i got a[x+(b/2a)]^2 - [(b^2)/4a] + c where h=-(b/2a) and k=c-[(b^2)/4a]
 


halvizo1031 said:
i got a[x+(b/2a)]^2 - [(b^2)/4a] + c where h=-(b/2a) and k=c-[(b^2)/4a]
Shouldn't h be + b/(2a)?
So f(x) = a(x + b/(2a))2 + c - b2/(4a)

Or, f(x) = a(x + h)2 + k, with h = b/(2a) and k = c - b2/(4a).

You know what the graph of y = g(x) = x2 looks like, right? How would you need to transform the graph of g to get the graph of f?
 

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