Shifting a graph to a new equation

  • Thread starter Vals509
  • Start date
  • Tags
    Graph
In summary, to shift a graph to a new equation, you can use a process called transformation which involves applying a set of rules to the original equation. The most common types of transformations used for shifting a graph are translation, reflection, dilation, and rotation. The type of transformation needed for a specific shift depends on its direction and distance. Multiple transformations can be used to shift a graph through composition of transformations. There are some special cases when shifting a graph, such as shifting along the x-axis or reflecting over the x-axis, where only one coordinate is changed while the other remains constant.
  • #1
Vals509
52
1

Homework Statement


how do you shift the graph y=x^2 to give the equation below


Homework Equations



y = 3(2x+1)^2 + 2

The Attempt at a Solution


I know it involves the following steps:
-shift the graph 2 units up
-shift 1 unit to the left
-dilate to the x-axis scale factor 0.5
-dilate the graph to the y-axis scale factor 3

Can someone pls confirm if the steps are in the right order. Help is greatly appreciated!
 
Physics news on Phys.org
  • #2
Those are the right steps- the order is irrelevant.
 

FAQ: Shifting a graph to a new equation

How do I shift a graph to a new equation?

To shift a graph to a new equation, you can use a process called transformation. This involves applying a set of rules to the original equation to create a new equation that results in a shifted graph.

What are the common types of transformations used to shift a graph?

The most common types of transformations used to shift a graph include translation, reflection, dilation, and rotation. These transformations can be applied to the x and y coordinates of the original equation to create a new equation.

How do I know which transformation to use for a specific shift?

The type of transformation you need to use for a specific shift depends on the direction and distance of the shift. For example, if you want to move the graph up or down, you would use a translation transformation by adding or subtracting a number to the original equation.

Can I use multiple transformations to shift a graph?

Yes, you can use multiple transformations to shift a graph. This is known as composition of transformations. You can apply one transformation after the other to achieve a desired shift in the graph.

Are there any special cases when shifting a graph?

Yes, there are some special cases when shifting a graph. For example, if you want to shift a graph along the x-axis, you would keep the y-coordinate constant and only change the x-coordinate using a translation transformation. Similarly, if you want to reflect a graph over the x-axis, you would keep the x-coordinate constant and only change the sign of the y-coordinate using a reflection transformation.

Similar threads

Graphing f(x)=√x but shifted 2 units to the left and then reflected
Replies
12
Views
6K
Am I understanding horizontal shift properly?
Replies
3
Views
1K
Graphical Transformations and Finding the Equation of a Curve
Replies
3
Views
1K
Finding the Parameters for the Curve y=asin(x-b)+c
Replies
11
Views
3K
Graphing sinusoidal tangent functions
Replies
17
Views
2K
Hi, I have a quick question about graph transformations.
Replies
2
Views
1K
Graphs of sin and cos, how to set points for x values
Replies
2
Views
2K
Where Do the Graphs of |3x-2| and 1/x Intersect and Diverge?
Replies
4
Views
2K
Suitable range of values for x
Replies
10
Views
2K
Order of permutations in transformations of functions
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top