If the graph of the function h defined by h (x) = 3x^2-8

is translated vertically upward by 9 units, it becomes the graph of a function f.

Find the expression for f (x).

There is no horiz. translation, so there is no change to "x" in h (x) = 3x^2-8; the graph does not shift horizontally. However, there is a change to y=h (x) when we add 9 to it: h (x) + 9 = 3x^2 - 8 + 9 becomes 3x^2 + 1. The vertex of this parabola is now at (0,1) instead of at (0,-8) as before.