Answer
$f(x)=3(x+1)^2-2$
Work Step by Step
Completing the square:
$f(x)=3x^2+6x+1$
$f(x)=3(x^2+2x)+1$
$f(x)=3(x^2+2x+(\frac{2}{2})^2)-3\cdot(\frac{2}{2})^2+1$
$f(x)=3(x^2+2x+1^2)-3\cdot1^2+1$
$f(x)=3(x+1)^2-3+1$
$f(x)=3(x+1)^2-2$
Graphing the function:
1st step (black graph): The parent function: $y=x^2$
2nd step (green graph): Stretch by a factor of 3. $y=3x^2$
3rd step (red graph): Shift 2 units down. $y=3x^2-2$
Final step (blue graph): Shift left by 1 unit. $y=3(x+1)^2-2$
