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: 12


Option (a)

Work Step by Step

The provided function, $x={{\left( y-5 \right)}^{2}}-2$ On comparing the above equation with $x={{\left( y-k \right)}^{2}}+h$ where $\left( h,k \right)$ is vertex, the vertex will be $\left( -2,5 \right)$. To find ordered pairs, choose values for $y$ on each side of the vertex. Then compute the values of $x$ and $y$ with the help of the given equation in below table. $\begin{matrix} x & y \\ -2 & 5 \\ 2 & 7 \\ 2 & 3 \\ 7 & 8 \\ 7 & 2 \\ \end{matrix}$ From the graph it can be found that this is the graph of a parabola which has the vertex $\left( -2,5 \right)$. Thus, (a).
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