Answer
The equation $y={{x}^{2}}+2x+3$
Work Step by Step
$y={{x}^{2}}+2x+3$ …… (1)
$\begin{align}
& x=-\frac{b}{2a} \\
& =-\frac{\left( 2 \right)}{2\cdot \left( 1 \right)} \\
& =-1
\end{align}$
Now for the y value put $x=-1$ in equation (1),
$\begin{align}
& y={{\left( -1 \right)}^{2}}+2\cdot \left( -1 \right)+3 \\
& =1-2+3 \\
& =2
\end{align}$
The vertex is $\left( -1,2 \right)$.
$\begin{matrix}
x & y \\
0 & 3 \\
-2 & 3 \\
-1 & 2 \\
1 & 6 \\
-3 & 6 \\
\end{matrix}$
