Write a function for the graph described as a transformation of y=x^2. 12. y=x^2 experiences a vertical stretch of factor 2 and then a shift right of 3 units.

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Write a function for the graph described as a transformation of y=x^2. 12. y=x^2 experiences a vertical stretch of factor 2 and then a shift right of 3 units.

Mathematics
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\[y=a(x-h)^2+k\] a = vertical stretch factor h = horizontal shift k = vertical shift
you don't have a vertical shift, so ignore the k = 0. Plug in the numbers for a and h.
\[y=2(x-3)^{2}\]

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is that right?
yes
thank you!
you're welcome
can you check another question i have? @peachpi
ok
y=x^2 experience a shift left by 2 units, then a horizontal shrink of factor 1/2 then a shift down 5 units my answer : y=(x-1/2)^2
horizontal shrinks/stretches are multiplied by the x from the inside. \[y=a(bx-h)^2+k\] Use that as your basic formula. a, h, and k are explained above. \(b\) is the horizontal shrink/stretch factor. The "default" numbers for a and b are 1, and for h and k it's 0. In your problem you have shift left, so h = -2 horizontal shrink, so b = 1/2 vertical shift down, so k = -5. They don't say anything about vertical stretch/shrink, so leave it as 1. \[y=\left( \frac{ 1 }{ 2 }x+2 \right)^2-5\]
thanks for explaining
you're welcome.
fyi pictures are better than words :) http://www.regentsprep.org/regents/math/algtrig/atp9/funclesson1.htm

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