- #1
trulyfalse
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Hello PF!
The graph of the function y = 2x2 + 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
y= af(1/b(x-h))+k
First I completed the square of y = 2x2 + x +1:
2x2 + x +1 = y
2(x2+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!
Homework Statement
The graph of the function y = 2x2 + 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
Homework Equations
y= af(1/b(x-h))+k
The Attempt at a Solution
First I completed the square of y = 2x2 + x +1:
2x2 + x +1 = y
2(x2+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!