Answer
Refer to the curve in Black in Graph I
Work Step by Step
For $f(x) = -3(x - 2)^2 + 1,$
when
$x = 4, y = -11;$
$x = 3, y = -2;$
$x = 2, y = 1;$
$x = 1, y = -2;$
$x = 0, y = -11$
As seen, $f(x) = -3(x - 2)^2 + 1$ is the horizontal translation to the right by 2 units, the vertical stretching by three times, the reflection across the $x$-axis and the vertical translation up by 1 unit of $f(x) = x^2$.
Domain = $(−\infty, \infty)$
Range = $(-\infty, 1]$
