## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

The equation $y={{x}^{2}}+2x+3$
$y={{x}^{2}}+2x+3$ …… (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 $\left( -1,2 \right)$. $\begin{matrix} x & y \\ 0 & 3 \\ -2 & 3 \\ -1 & 2 \\ 1 & 6 \\ -3 & 6 \\ \end{matrix}$