Answer
The graph for the equation $y={{x}^{2}}+2x+1$.
Work Step by Step
$y={{x}^{2}}+2x+1$ (equation - 1)
$\begin{align}
& x=-\frac{b}{2a} \\
& =-\frac{2}{2\cdot \left( 1 \right)} \\
& =-1
\end{align}$
Now for the y value put $x=-1$ in equation (1).
$\begin{align}
& y={{\left( -1 \right)}^{2}}+2\cdot \left( -1 \right)+1 \\
& =1-2+1 \\
& =0
\end{align}$
The vertex is $\left( -1,0 \right)$.
Now choose some value of x on both sides of the vertex and compute the corresponding y value.
$\begin{matrix}
x & y \\
1 & 4 \\
0 & 1 \\
-1 & 0 \\
-2 & 1 \\
-3 & 4 \\
\end{matrix}$
