Question

List a sequence of transformations which maps the graph of y=x^2 to the image with equation y=4*(2x-3)^2 + 1

Answer 1

The general transformation equation is:
g(x)=a*f(b(x-h))+k

where
h=horizontal translation (right if h>0)
b=horizontal scaling (stretch if 1/b>1)
a=vertical scaling (stretch if a>1)
k= vertical translation (up if k>0)

applied in the above order, i.e. according to the PEMDAS rule.

So the transformed equation can be written as:
let f(x)=x²
then
g(x)=4*(2x-3)² + 1
=4*(2(x-3/2))² +1
=4*f(2(x-3/2))+1

Identify the values of h,b,a,k as given above and hence the sequence of transformations.