Explanation Given: The equation of parabola is, ( y − 2 ) 2 = 4 ( x + 2 ) Approach: The following equation is the basic equation for an parabola that is not centered at the origin. ( x − h ) 2 = 4 p ( y − k ) or ( y − k ) 2 = 4 p ( x − h ) With the following properties, Vertex V = ( − h , − k ) …… ( 1 ) Focus F = ( − h , p − k ) or F = ( p − h , − k ) …… ( 2 ) Directrix y = − p − k or x = − p − h …… ( 3 ) Calculation: Consider the equation, ( y − 2 ) 2 = 4 ( x + 2 ) Compare the equation of the parabola with the standard equation. h = − 2 p = 1 k = 2 Calculate the vertex of the parabola To determine (b) To sketch: The graph of the parabola and its directrix.

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Chapter 12.CR, Problem 7E

To determine

(a)

To find:

The vertex, focus, and directrix of the parabola.

To determine

(b)

To sketch:

The graph of the parabola and its directrix.

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Chapter 12.CR, Problem 6E

Chapter 12.CR, Problem 8E

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Chapter 12 Solutions

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(a) To find: The vertex, focus, and directrix of the parabola.

Solution Summary: The author explains the basic equation for a parabola that is not centered at the origin.