Which steps transform the graph of y=x^2 to y=-2(x- 2)^2+ 2?

1 Answer
Jun 25, 2018
  1. Reflection over the y-axis.
  2. Vertical stretch by a factor of two.
  3. Horizontal translation right two units.
  4. Vertical translation up two units.

Explanation:

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.