Question

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)?

Answer 1

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