Question 1037681
Dilate by two units in the direction of the y axis means y turns to 2y

{{{2y = 2x^2 + 1}}}

Reflect about y = x 
means x and y are exchanged thus we get
{{{2x = 2 y^2 + 1}}}

Rotate anticlockwise by 90 degrees means x-1 turns into y-3 and y-3 into -(x-1).

{{{2x-2 = 2y^2 -1 = 2(y-3)^2 + 12 y - 18 - 1}}}
{{{2(x-1) = 2(y-3)^2 + 2(y-3)  - 13}}}
{{{2(y-3)= 2(x-1)^2 - 2 (x-1) - 13}}}
{{{2y - 6 = 2x^2 - 4x + 2 - 2x +2 -13}}}
{{{2y = 2x^2 - 6x -3}}}
{{{y = x^2 -3x -3/2}}}