Suppose the graph of y=x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
(a)
(b)
When you translate a coordinate, say x, you replace it with a shifted value in the "opposite" direction.
In the case of a) you are shifting the parabola down by 3, so we need to add 3 to the y-coordinate:
$\displaystyle y = x^2 \to y + 3 = x^2$
or
$\displaystyle y = x^2 - 3$
In the case of b) you are shifting the parabola 4 units in the +x direction, so you want to subtract 4 from the x coordinate.
$\displaystyle y = x^2 \to y = (x - 4)^2$
-Dan