Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - 10.2 The Parabola - 10.2 Assess Your Understanding - Page 647: 58

Answer

$(x-1)^2=2-y$

Work Step by Step

If the major axis of the parabola is parallel to the y-axis then it is in the form of $4k(y-a)=(x-b)^2$, where $(b,a)$ is the vertex of the parabola and $k$ is a constant (positive if open up, negative if open down). If the major axis of the parabola is parallel to the x-axis then it is in the form of $4k(x-a)=(y-b)^2$, where $(a,b)$ is the vertex of the parabola and $k$ is a constant. (positive if open right, negative if open left). Here the major axis is parallel to the y-axis and the vertex is in $(1,2)$. Thus the equation becomes $(x-1)^2=4k(y-2)$. We also know that $(2,1)$ is on the graph, hence plugging in $x=2,y=1$ gives us: $(2-1)^2=4k(1-2)\\1=-4k\\k=-\frac{1}{4}$. Hence our equation: $(x-1)^2=4-(\frac{1}{4})(y-2)\\(x-1)^2=-(y-2)\\(x-1)^2=2-y$
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