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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 13 - Conic Sections - 13.1 Conic Sections: Parabolas and Circles - 13.1 Exercise Set - Page 854: 18

Answer

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