In words describe the transformation that occurs: g(x)=(x-2) ^2

Question

Choose from the following functions:

 g (x)=(x-2)² ;   (2). h(x) = x ²  - 2 ;   (3).  (x)=(x+3) ² ;       (4).  j(x) = (x+1)²  + 3

In words, describe the  transformation that occurs on a graph (example: A graph of f(x) = x²  shows the graph of f (x) is sifted 6 units to the left), In a parabola shape form, etc...

Answer 1

So I'm a little unclear about the statement of the question, but I'll assume we are to show how transformations can be applied to f(x) = x² to obtain g(x), h(x), i(x), and j(x). 

 

g(x) = (x-2)² is f(x) = x² shifted 2 units to the right (because we substitute x with x-2), so its graph is a parabola opening up with a vertex at (2,0).

 

h(x) = x² - 2 is f(x) = x² shifted 2 units down (because we subtract a 2 from f(x)), so its graph is a parabola opening up with a vertex at (0,-2).

 

i(x) = (x+3)² is f(x) = x² shifted 3 units to the left (because we substitute x with x+3), so its graph is a parabola opening up with a vertex at (-3,0).

 

j(x) = (x+1)² + 3 is f(x) = x² shifted 1 unit to the left and 3 units up (because we substitute x with x+1 and then add 3), so its graph is a parabola opening up with a vertex at (-1,3).