we have
f(x)=x^2
this is a vertical parabola with vertex at (0,0)
and
we have
g(x)=2(x+1)^2-7
this is a vertical parabola with vertex at (-1,-7)
so
the transformation of f(x) to g(x) is equal to
(0,0) ------> (-1,-7)
the rule of the translation is equal to
(x,y) --------> (x-1, y-7)
that means ------> the translation is 1 unit at left and 7 units down
and we have a second transformation
(x,y) -------> (ax, y)
the factor a is 2
therefore
First transformation
x^2 --------> 2x^2
second transformation
2x^2---------> 2(x+1)^2-7
