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.