The graph of f (x) = 2x^2 - 3x + 5 will be translated 8 units down, producing the graph of q (x). What equation represents the new function, q (x) ?

In general, to translate h units right, and k units up, we have

q (x) = f (x-h) + k

Here, h=0, k=-8, so

to translate f (x) 8 units down, we have

q (x) = f (x-0) - 8

=2x^2-3x+5-8

=2x^2-3x-3