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#.