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August 13th, 2017, 05:39 AM   #1
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Quadratic Transformations

I was taught that the only order one had to keep in mind when doing quadratic transformations was to do the vertical transformations (vertical translations, reflections on the $\displaystyle x$ axis, stretching and compressing) separate from horizontal transformations (horizontal translations).

The question asks to transform the point (-4,16) from the graph $\displaystyle y =
x^2$ to the graph $\displaystyle y = 2(x-3)^2 -8$.



The Transformations:

1. Horizontal translation 3 units to the right.
2. Stretch by a factor of 2.
3. Vertical translation 8 units down.


Changes to the point as it transforms:


(-4,16)
1. (-1,16)
2. (-1,32)
3. (-1,24)

However, if I do all of the steps in the opposite order I get a different final point:

(-4,16)
3. (-4,8 )
2. (-4,16)
1. (-1,16)

I have done all of the horizontal transformations (step 1.) separate from the vertical ones(steps 2. and 3.), only to get a different answer. What am I doing wrong guys?
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August 13th, 2017, 07:08 AM   #2
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You were clearly taught wrong then.
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August 13th, 2017, 07:29 AM   #3
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Yes, I was. I should have done the effects of "a" before the effects of "k".
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