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: 37

Answer

Vertex: $(0,0)$ Focus: $(0,1)$ Directrix: $y=-1$ See graph

Work Step by Step

We are given the parabola: $x^2=4y$ The standard form of the equation is: $(x-h)^2=4p(y-k)$ Determine $h,k,p$: $h=0$ $k=0$ $4p=4\Rightarrow p=1$ Determine the vertex: $(h,k)=(0,0)$ Determine the focus: $(h,k+p)=(0,0+1)=(0,1)$ Determine the directrix: $y=k-p$ $y=0-1$ $y=-1$ Determine the latus rectum points: $y=1$ $x^2=4(1)$ $x^2=4$ $x=\pm 2$ $\Rightarrow (-2,1),(2,1)$ Plot the points, plot the directrix, and graph the parabola:
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