SOLUTION: If the function y=x^2 is dilated in the x direction by a factor of 5, dilated in the y direction by a factor of 2, translated 3 to the right and translated 4 up, then type its equa

Algebra ->  Equations -> SOLUTION: If the function y=x^2 is dilated in the x direction by a factor of 5, dilated in the y direction by a factor of 2, translated 3 to the right and translated 4 up, then type its equa      Log On


   

Question 1118148: If the function y=x^2 is dilated in the x direction by a factor of 5, dilated in the y direction by a factor of 2, translated 3 to the right and translated 4 up, then type its equation.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The original function is y+=+x%5E2.

(1) dilated in the x direction by a factor of 5: replace x with x/5: y+=+%28x%2F5%29%5E2

(2) dilated in the y direction by a factor of 2: replace y with y/2: y%2F2+=+%28x%2F5%29%5E2, or y+=+2%28x%2F5%29%5E2

(3) translated 3 to the right: replace x with x-3: y+=+2%28%28x-3%29%2F5%29%5E2

(4) translated 4 up: add 4 to y: y+=+2%28%28x-3%29%2F5%29%5E2%2B4

A graph:

red: basic function
green: dilated by a factor of 5 in the x direction (red, 1/5 as steep)
blue: dilated by a factor of 2 in the y direction (green, 2 times as steep)
purple: translated 3 to the right (blue, moved right 3)
yellow: translated 4 up (purple, moved up 4)