Question

How is the graph of y=2[(3)^x-1]+4 translated from the graph of y=2(3)^x?
A)1 unit right and 4 units up
B) 4 units left and 1 unit down
C) 4 units right and 1 unit up
D) 1 unit left and 4 units down

Answer 1

Complete the square by taking half of the coefficient of x and squaring it, then add it to both sides and rearrange to isolate y again:

y + 1/4 = x^2 - x + 1/4 - 3 = (x -1/2)^2 - 3
y = (x - 1/2)^2 - 13/4

If you think of this as translating the graph of x^2 down and to the right, you can just draw the graph of x^2 so that the vertex is at (1/2, -13/4) instead of the origin.
here to jog your memory: http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/geometry/graphtranslationiandstretch.html

Answer 2

A)1 unit right and 4 units up