Answer
Refer to the curve in Black in Graph I
Work Step by Step
For $f(x) = 2(x - 2)^2 - 4,$
when
$x = 4, y = 4;$
$x = 3, y = -2;$
$x = 2, y = -4;$
$x = 1, y = -2;$
$x = 0, y = 4$
As seen, $f(x) = 2(x - 2)^2 - 4$ is the horizontal translation to the right by 2 units, the vertical stretching twice and the vertical translation down by 4 units of $f(x) = x^2$.
Domain = $(−\infty, \infty)$
Range = $[-4, \infty)$
