For a function y=f(x), a transformed graph of f has the equation y = a f( b(x-h))+k.
a represents the vertical stretches (by a factor of |a|) and any x-axis reflections (if a<0)
b represents the horizontal stretches (by a factor of |1/b|) and any y-axis reflections (if h<0)
h represents horizontal translations (h>0 means translate right; h<0 means translate left)
k represents vertical translations (k>0 means translate up; k<0 means translate down)
So if y=x^2, then y= -f(2x) = -(2x)^2
Reflection in x-axis, then horizontal compression by a factor of 1/2.
To graph this, graph y=x^2 first, then reflect it in the y-axis (multiply all y-coordinates of points by -1). Then horizontally compress it by a factor of 1/2 by multiplying all x-coordinates of the points by 1/2.
