# Determine its image point after the transformation

• MHB
• Azurin
In summary: I assumed the latter.In summary, the graph of y=x^2 was transformed to the graph of y=-3(x+5)^2-2. The point (-3, 9) on the original graph was transformed to the image point (2, -29) after the transformations were applied. The mapping rule for points on the graph y=x^2 to y=-3(x+5)^2-2 is (x,y) -> (x+5, -3y-2). This is known as the vertex form of a quadratic equation.
Azurin
The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2. The point (-3, 9) lies on the graph of y=x^2. Determine its image point after the transformations.

Azurin said:
Azurin said:
The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2. The point (-3, 9) lies on the graph of y=x^2. Determine its image point after the transformations.
Skeeter is assuming the function is $$\displaystyle y= -3(x+5)^2- 2$$, not $$\displaystyle y= -3(x+5) 2$$.
Is that correct?

If so, I would observe that x has 5 added to it and that y (everything done after the squaring) is multiplied by -3 then had 2 subtracted. that is, (x, y) is transformed to (x+ 5, -3y- 2). In particular (-3, 9) is transformed to (-3+ 5, -3(9)- 2)= (2, -29).

Check- yes, if x= 2, $$\displaystyle y= -3(-2+ 5)^2- 2= -3(3)^2- 2= -27- 2= -29$$.

Last edited:
You wrote
The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2.

Did you mean "y= -3(x+ 5)^2- 2" or just "y= -3(x+ 5)^2"? In other words, did you drop the "^" or did you type "-" instead of "^"?

## 1. What is a transformation in the context of determining an image point?

A transformation is a mathematical operation that maps one set of points onto another set of points. In the context of determining an image point, it refers to the process of finding the new location of a point after applying a specific transformation function.

## 2. What are the different types of transformations that can be used to determine an image point?

There are several types of transformations that can be used, including translation, rotation, reflection, dilation, and shear. Each type of transformation has a unique effect on the position and orientation of the image point.

## 3. How do I determine the image point after a transformation?

To determine the image point after a transformation, you will need to know the coordinates of the original point and the transformation function being applied. You can then use the transformation function to calculate the new coordinates of the image point.

## 4. Can a transformation change the size or shape of an image point?

Yes, a transformation can change the size or shape of an image point. This depends on the type of transformation being used. For example, a dilation transformation will change the size of the image point, while a shear transformation will change its shape.

## 5. What is the purpose of determining an image point after a transformation?

The purpose of determining an image point after a transformation is to understand how the transformation affects the position and properties of the original point. This can be useful in various fields such as geometry, computer graphics, and image processing.

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