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1. The problem statement, all variables and given/known data

The graph of the function y = 2x^{2}+ x +1 is stretched vertically about the x-axis by a factor of 2, stretched horizontally about the y-axis by a factor of 1/3 and translated 2 units right and 4 units down. Write the equation of the transformed function

2. Relevant equations

y= af(1/b(x-h))+k

3. The attempt at a solution

First I completed the square of y = 2x^{2}+ x +1:

2x^{2}+ x +1 = y

2(x^{2}+1/2x+1/16-1/16)+1=y

2(x+1/4)^{2}+14/16=y

Then, using mapping notation I calculated what the new x and y coordinates would be on the transformed function:

(x,y) → (1/3x+2,2y-4)

Therefore, the point (-2,7) → (4/3,10)

Using the aforementioned equation I transformed the function:

a=2

b=1/3

h=2

k=-4

y=2(2(3(x-7/4)^{2})-25/8)

However, when I input the new function into my calculator I received the values (-2,7) → (4/3,53/9) which is demonstrated to be incorrect. Is there a way to solve this problem without putting the function in the form y= af(1/b(x-h))+k? If possible, can anyone show me how to derive the correct equation for the transformed function after completing the square of the function? Thanks!

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# Homework Help: Combining Transformations; Completing the Square

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