SOLUTION: Let f (x) = (x^2 − 2x + 1)/(20) The graph of function g is created by stretching the graph vertically by a factor of 40, then shifting the graph of f down 6 units, an

Algebra ->  Trigonometry-basics -> SOLUTION: Let f (x) = (x^2 − 2x + 1)/(20) The graph of function g is created by stretching the graph vertically by a factor of 40, then shifting the graph of f down 6 units, an      Log On


   

Question 933049: Let f (x) = (x^2 − 2x + 1)/(20)

The graph of function g is created by
stretching the graph vertically by a factor of 40,
then shifting the graph of f down 6 units,
and finally shifting the graph right 5 units .
Find the function g.
g(x) =
Please help
Thank you
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
That starts as f%28x%29=%281%2F20%29%28x-1%29%5E2.

Your transforming description goes this way:
40%2A%281%2F20%29%28x-1%29%5E2
2%28x-1%29%5E2
;
2%28x-1%29%5E2-6
;
2%28x-1-5%29%5E2-6
highlight%28g%28x%29=2%28x-6%29%5E2-6%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f+%28x%29+=+%28x%5E2-2x+%2B+1%29%2F20
"stretching the graph vertically by a factor of 40" means we go from f%28x%29 to 40%2Af%28x%29
"then shifting the graph of f%28x%29 down 6 units" has us tacking on a "-6" like this: 40%2Af%28x%29-6

"and finally shifting the graph right 5 units " tells us to replace 'x' with 'x-5' to get 40%2Af%28x-5%29-6


Therefore, g%28x%29=40%2Af%28x-5%29-6
f+%28x-5%29+=+%28%28x-5%29%5E2+-2%28x-5%29+%2B+1%29%2F20
f+%28x-5%29+=+%28x%5E2-10x%2B25-2x%2B10+%2B+1%29%2F20
f+%28x-5%29+=+%28x%5E2-12x%2B36%29%2F20
g%28x%29=40%2A%28x%5E2-12x%2B36%29%2F%2820%29+-6
g%28x%29=cross%2840%292%2A%28x%5E2-12x%2B36%29%2Fcross%2820%29+-6
g%28x%29=2%28x%5E2-12x%2B36%29+-6
g%28x%29=2x%5E2-24x%2B72+-6
g%28x%29=2x%5E2-24x%2B66