Answer
See image
Work Step by Step
Write $f$ in the form $f(x)=a(x-h)^{2}+k$:
$\begin{aligned}f(x)&=3x^{2}+6x\\&=3\left(x^{2}+2x\right)\\&=3\left(x^{2}+2x+1\right)-3\\&=3(x+1)^{2}-3\end{aligned}$
Let $f_{1}(x)=x^{2}$.
Then, $f(x)=3f_{1}(x+1)-3$.
The graph is obtained from $f_{1}(x)$ by
- vertical stretching by factor $3,$
- shifting to the left by 1 unit,
- and then down by 3 units
Point by point,
$\left[\begin{array}{lllll}
(x,y) & \rightarrow & (x,3y) & \rightarrow & (x-1,3y-3)\\
& & & & \\
(0,0) & \rightarrow & (0,0) & \rightarrow & (-1,-3)\\
(-1,1) & \rightarrow & (-1,3) & \rightarrow & (-2,0)\\
(1,1) & \rightarrow & (1,3) & \rightarrow & (0,0)\\
(-2,4) & \rightarrow & (-2,12) & \rightarrow & (-3,9)\\
(2,4) & \rightarrow & (2,12) & \rightarrow & (1,9)
\end{array}\right]$
