Hi, I have a quick question about graph transformations.

In summary, to obtain the equation f(x)=-(3+x)^2+1 from the graph of y=x^2, you need to move the graph 3 units to the left, reflect it about the x-axis, and then move it up 1 unit. To show this transformation algebraically, you can define new variables x' and y' and manipulate the equation to resemble the standard form y=x^2.
  • #1
Faith S
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Member has been warned not to remove the template.
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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  • #2
Define an x' and a y' so that your equation looks like the y=x^2 format.
 
  • #3
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?
 

1. What are graph transformations?

Graph transformations refer to the process of changing the shape or position of a graph on a coordinate plane. This can be done through translations, reflections, rotations, or dilations.

2. Why are graph transformations important?

Graph transformations are important because they allow us to visually understand and analyze data by manipulating the graph. They also make it easier to compare and contrast different data sets.

3. How do I perform a graph transformation?

The specific steps for performing a graph transformation vary depending on the type of transformation. Generally, you will need to determine the type of transformation, identify the key points on the graph, and apply the appropriate formulas or rules to transform the graph.

4. What is the difference between a reflection and a rotation?

A reflection is a transformation that flips a graph across a line of symmetry, while a rotation is a transformation that turns a graph around a fixed point. In other words, a reflection produces a mirror image of the original graph, while a rotation produces a graph that is rotated in a circular motion.

5. Can graph transformations affect the accuracy of my data?

No, graph transformations do not affect the accuracy of the data itself. They only change the representation of the data on a graph. However, incorrect transformations or misinterpretation of the transformed graph can lead to inaccurate conclusions about the data.

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