SOLUTION: vertically compress by a factor of 1/2 and translate down by 2 y=x^2

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Question 866555: vertically compress by a factor of 1/2 and translate down by 2
y=x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We start with y=x%5E2. That is given to us. This is the parent quadratic function/equation. This is the green graph shown below.


We would then "vertically compress by a factor of 1/2". So we would multiply x%5E2 by 1/2 which "squishes" the graph. This is because every point on the graph is now half as high as it used to be (ex: y = 4 ---> y = (1/2)*4 = 2 )


So we now have y+=+expr%281%2F2%29x%5E2. This is the blue graph shown below.


Finally, we "translate down by 2" to get y+=+expr%281%2F2%29x%5E2-2. Visually we are just shifting the entire blue graph 2 units down to get the purple graph.


Below are the graphs of y=x%5E2, y+=+expr%281%2F2%29x%5E2, and y+=+expr%281%2F2%29x%5E2-2 in green, blue and purple respectively.




The sequence of graphs above (all plotted on the same xy axis) shows us how y=x%5E2 transforms into y+=+expr%281%2F2%29x%5E2-2