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: 9

Answer

part $\left( c \right)$

Work Step by Step

The standard form of the equation of the parabola vertex of the parabola at $\left( h,k \right)$ is defined as, $y=a{{\left( x-h \right)}^{2}}+k$ Compare the provided equation with the standard form of the equation of the circle. It shows that the provided equation is the equation of a circle. The values of $h\text{ and }k$ are obtained as: $\begin{align} & x-h=x-2 \\ & -h=-2 \\ & h=2 \end{align}$ And, $k=-5$ So, the vertex of the parabola is obtained as $\left( 2,-5 \right)$. The correct match for the graph of the equation $y={{\left( x-2 \right)}^{2}}-5$ is graph (c).
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