Question

What is the transformations of f(x)=(x-2)^2-4

Answer 1

This is how to solve the problem: "What is the transformations of f(x)=(x-2)^2-4"

Looking at the quadratic equation given,
f(x)  = (x-2)^2 - 4
It's like seeing product of sum and difference of two squares.

(x-2)^2 - 4
[ (x-2) - 2 ] [ (x-2) + 2 ]
[ x - 2 - 2 ] [ x - 2 + 2 ]
[ x - 4 ] [ x ]
[ x^2 - 4x ]

So the final transformation of f(x) = (x-2)^2 -4 is f(x) = (x^2 - 4x). 
In this way, we are able to show how a complicated equation to simple yet equal equation in quadratic form.