Answer
$f(x)=3(x+1)^2-2$
See graph
Work Step by Step
We are given the function:
$f(x)=3x^2+6x+1$
Complete the square:
$f(x)=3(x^2+2x)+1=3(x^2+2x+1)-3+1=3(x+1)^2-2$
We start graphing with the basic function $a(x)=x^2$.
We horizontally shift $a(x)$ by one unit to the left to get $b(x)=(x+1)^2$.
Then we vertically stretch $b(x)$ by a factor of 3 to get $c(x)=3(x+1)^2$.
Finally we vertically shift $c(x)$ 2 units downward to get $f(x)=3(x+1)^2-2$.
We use 3 points: $(-2,1),(-1,-2),(0,1)$
