List a sequence of transformations which maps the graph of y=x^2 to the image with equation y=4*(2x-3)^2 + 1
Please help
y = 4(2(x-3/2))^2+1
shift right 3/2
horizontal shrink by 2
vertical stretch by 4
shift up 1
or
y=16(x-3/2)^2+1
shift right 3/2
vertical stretch by 16
shift up 1
I still do not understand, pardon me
Could u use the terms dilation, reflection and translation and the axes?
stretch = dilation
shift = translation
there is no reflection involved.
It amazes me that you could not figure that out. I assume you know that x is horizontal and y is vertical...
Keith, please refrain from using different screen names.
Also, please mention that you are reposting the question, and reposting within a short time could mean duplicate efforts by tutors, and hence slow the answering process.
Your previous question has also been answered here:
http://www.jiskha.com/display.cgi?id=1482466342
To map the graph of y = x^2 to the equation y = 4*(2x - 3)^2 + 1, we can use a sequence of transformations. Let's break it down step by step:
1. Horizontal Stretch or Compression: The expression inside the parentheses, (2x - 3), suggests that we have a horizontal stretch or compression. In this case, it is a horizontal compression by a factor of 2. This means that the graph will be narrower.
2. Horizontal Translation: The expression (2x - 3) inside the parentheses also indicates a horizontal translation by 3 units to the right. This means that the graph will shift to the right by 3 units.
3. Vertical Stretch: The coefficient 4 in front of the parentheses indicates a vertical stretch by a factor of 4. This means that the graph will be taller.
4. Vertical Translation: Finally, the constant term (+1) outside the parentheses indicates a vertical translation by 1 unit upwards. This means that the graph will shift upwards by 1 unit.
So, the sequence of transformations to map the graph of y = x^2 to the equation y = 4*(2x - 3)^2 + 1 is:
1. Horizontal Compression by a factor of 2.
2. Horizontal Translation to the right by 3 units.
3. Vertical Stretch by a factor of 4.
4. Vertical Translation upwards by 1 unit.
Applying these transformations to the original graph will give you the graph represented by the equation y = 4*(2x - 3)^2 + 1.