Hi, I have a quick question about graph transformations.

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SUMMARY

The discussion centers on transforming the graph of the function y=x^2 into the function f(x)=-(3+x)^2+1. The transformation involves three key steps: shifting the graph 3 units to the right, reflecting it across the x-axis, and then translating it 1 unit upwards. Participants emphasize the importance of defining new variables, x' and y', to facilitate the manipulation of the equation into the standard form of y=x^2. The discussion highlights the need for clarity in understanding the direction of graph movements.

PREREQUISITES
  • Understanding of quadratic functions and their graphs
  • Knowledge of function transformations (translations, reflections)
  • Familiarity with variable substitution in equations
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the principles of function transformations in detail
  • Learn how to apply variable substitution in graph transformations
  • Explore examples of quadratic function transformations
  • Practice graphing transformations using graphing software like Desmos
USEFUL FOR

Students learning algebra, educators teaching graph transformations, and anyone seeking to deepen their understanding of quadratic functions and their manipulations.

Faith S
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One of my homework questions said "Explain how to obtain f(x)=-(3+x)^2+1 from the graph of y=x^2."
I know somehow you need to move the graph right 3, reflect about the x-axis, and move up one, but I don't know how to factor and manipulate the equation to show this.
 
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Define an x' and a y' so that your equation looks like the y=x^2 format.
 
Faith S said:
One of my homework questions said "Explain how to obtain f(x)=-(3+x)^2+1 from the graph of y=x^2."
I know somehow you need to move the graph right 3, reflect about the x-axis, and move up one, but I don't know how to factor and manipulate the equation to show this.

Your description is perfectly OK as is. However, be careful about moving the graph---right or left?
 

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