SOLUTION: The graph of y = x^2 is stretched vertically by a factor of 3, stretched horizontally by a factor of 5, and translated horizontally to the left by 12. Determine the equation that r

Algebra ->  Functions -> SOLUTION: The graph of y = x^2 is stretched vertically by a factor of 3, stretched horizontally by a factor of 5, and translated horizontally to the left by 12. Determine the equation that r      Log On


   

Question 1175361: The graph of y = x^2 is stretched vertically by a factor of 3, stretched horizontally by a factor of 5, and translated horizontally to the left by 12. Determine the equation that results from these transformations.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Original graph: y = x^2

graph%28400%2C200%2C-20%2C10%2C-5%2C25%2Cx%5E2%29

Stretch vertically by a factor of 3: the y value gets multiplied by 3: y = 3x^2

graph%28400%2C200%2C-20%2C10%2C-5%2C25%2Cx%5E2%2C3x%5E2%29

Stretch horizontally by a factor of 5: to get a horizontal stretch of 5, the x value has to be DIVIDED by 5: y = 3(x/5)^2

graph%28400%2C200%2C-20%2C10%2C-5%2C25%2Cx%5E2%2C3x%5E2%2C3%28x%2F5%29%5E2%29

Translated left 12: replace "x" with "x+12": y = 3((x+12)/5)^2



ANSWER: The final equation is

y = 3((x+12)/5)^2