Check the picture below, which is just a template for transformations.
so hmmm if we grab f(x) and move it downwards by 8 units, that means that the value for "D" gets a -8 added to it, so let's do that.
[tex]f(x)=3x^2+1\qquad \implies f(x)=\stackrel{A}{3}(\stackrel{B}{1}x+\stackrel{C}{0})^2+\stackrel{D}{1} \\\\\\ g(x)=3(1x+0)^2+1+(-8)\implies {\LARGE \begin{array}{llll} g(x)=3x^2-7 \end{array}}[/tex]
