The transformation #g(x)# of a polynomial function #f(x)# takes the form:

#g(x) = af[k(x-d)]+c#

#a# is the factor of vertical stretch or compression. If #a# is negative, then the transformed graph is reflected over the #y#-axis.

#1/k# is the factor of horizontal stretch or compression. If #k# is negative, then the transformed graph is reflected over the #x#-axis.

#d# is the horizontal translation.

#c# is the vertical translation.

When looking at a transformation, the steps are applied moving from the left side of the equation to the right.

In #y=-2(x-2)^2+2#:

#a = -2#. The graph is reflected over the #y#-axis and stretched vertically by a factor of 2.

#d# = 2. The graph is translated two units to the right.

#c# = 2. The graph is translated two units upwards.