transformations question

[Thymaster]

the transformation t:R^2>R^2 is defined by
T([x y])=[30 02]+[14]
the image of the curve y=2x^2+1 under the transformation T has an equation y=ax^2+bx+c
find a b c

[BubbleWrapMan]

(x,y) -> (3x+1, 2y+4)

Let x' = 3x+1 and y' = 2y+4

Then x = (x'-1)/3 and y = (y'-4)/2

Hence (y'-4)/2 = 2( (x'-1)/3 )^2 + 1

Then just rearrange