A graph has equation y=2x^2-4. What is the equation of the new graph when it is translated 2 units in the positive x direction

Question

anonymous · Answer

2 units to the right is $$f(x-2)$$
$$y=2(x-2)^{2}-4$$

anonymous · Answer

these can be opened to
$$y=2x^2-8x+4$$

anonymous · Answer

these can be seen as the TP(0;-4) is now (2;-4)

anonymous · Answer

do any of u mind explaining?:D

anonymous · Answer

translating a graph can be done in two ways
>shifting it along the y-axis which affects 
$$f(x)$$
if a graph is moved 2 units up
$$f(x)+2$$
$$y=2x^2-4+2$$
and two units down
$$f(x)-2$$
$$y=2x^2-4-2$$
>but when pelleting along the x-axis it is always oppsite 
ie.2 units right(the positive x direction)
affects x$$f(x-2)=2(x-2)^2-4$$
ie.2 units left(the positive x direction)
affects x$$f(x+2)=2(x+2)^2-4$$

anonymous · Answer

why is it f(x-2)?

turingtest · Answer

$$f(x-a)$$shifts the graph of $f(x)$ by $a$ units to the right
why? consider some random graph...|dw:1341710473045:dw|at x=a I have marked the point
now what about the graph of $f(x-a)$ ?
well, if we change our graph from f(x) to f(x-a) then the point f(a) becomes f(a-a)=f(0)
so the point that was at x=a is now f(0) instead of f(a)
let's see what that looks like...