A vertical stretch appears as a multiplier for the function value. Translation right appears as a value subtracted from the independent variable. Translation up appears as a value added to the function value.
For function f(x), stretching by a factor of 2, then translation 5 right and -1 up will give the function
... g(x) = 2f(x-5) -1
When f(x) = x², this becomes ...
... g(x) = 2(x -5)² -1
... g(x) = 2x² -20x +49
