transforming the graph of the parent quadratic function . i have no clue what any of this means or how to do it

Question

describe how to transform the graph of F(x)=x2 to obtain the graph of the relation function g(x)=f(-4(x-3))+1.

Answer 1

f(x) = x²

The transformations are:

g(x) = a·(b(x-c))² + d

1. a = vertical stretch by factor of a. If a<0, reflects graph across x -axis
2. b = horizontal stretch by a factor of 1/b. If b<0, reflects graph across y-axis
3. c = horizontal shift (left/right)
4. d = vertical shift (up/down)

Your graph is:

g(x) = f(-4(x-3) + 1 = (-4(x-3))² + 1

1. a = 1 no vertical stretch
2. b = -4 horizontal stretch by a factor of -1/4, reflects graph across the y-axis
3. c = 3 shifts graph right 3 units
4. d = 1 shifts graph up 1 unit