Question 1170916
The function translation / transformation rules:

{{{f(x) + b}}} shifts the function {{{b}}} units {{{upward}}}

{{{f(x) -b}}} shifts the function {{{b}}} units {{{downward}}}

{{{f(x + b)}}} shifts the function {{{b}}} units to the {{{left}}}

{{{f(x-b)}}} shifts the function {{{b }}}units to the {{{right}}}

{{{-f(x)}}} reflects the function in the {{{x}}}-axis (that is, {{{upside-down}}})

{{{f(-x)}}} reflects the function in the {{{y}}}-axis (that is, swapping the left and right sides).


so, what transformations turn {{{y = x^2}}} into {{{y= -2(x - 1)^2+ 3}}}


{{{-2}}}: reflects the function in the {{{x}}}-axis (that is, {{{upside-down}}})

{{{(x-1)}}}: shifts the function {{{1}}} unit to the {{{right}}}

+{{{ 3}}}: shifts the function {{{3}}} units {{{upward}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
locate(-2,3,y=x^2), locate(2,2,y=-2(x - 1)^2+ 3),
graph( 600, 600, -10, 10, -10, 10, -2(x - 1)^2+ 3, x^2)) }}}