Answer
graph C
Work Step by Step
The standard form of the given quadratic function, $f(x)=
x^2+4x+3
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( x^2+4x \right)+3
\\\\
f(x)=\left( x^2+4x+\left( \dfrac{4}{2} \right)^2 \right)+3-\left( \dfrac{4}{2} \right)^2
\\\\
f(x)=\left( x^2+4x+4 \right)+3-4
\\\\
f(x)=\left( x+2 \right)^2-1
.\end{array}
Since the vertex of $f(x)=a(x-h)^2+k$ is at $(h,k)$, then the vertex of the equation above is $(
-2,-1
).$ Hence, it corresponds to $\text{
graph C
}.$
