The graph shows the parabolas

Given that $g(x)$ is a translation of $f(x),$ find an expression for $g(x).$

If you know an expression for $f(x)$, you can then find $g(x).$ Look at the location of the vertices to find how much to translate $f$ by, both horizontally and vertically, to get $g.$

Since the curve $y=f(x)$ is a parabola, $f(x)$ is a quadratic, so it has the form

We know that $(-6,0),(-3,-9)$ and $(0,0)$ lie on $y=f(x)$ and so we can substitute this information into $y=f(x)$ to find $a,b$ and $c$ - thus, we find an expression for $f(x).$