(a) Explanation Definition used: “The equation of shifted parabola with vertex V ( h , k ) is ( y − k ) 2 = 4 p ( x − h ) ”. “The equation of the parabola with vertex V ( 0 , 0 ) , focus F ( p , 0 ) and directrix x = − p is y 2 = 4 p x ”. “If h and k are any two positive real numbers and a graph of any equation is in terms of x and y then. ( i ) Replacing x by x − h , shift the graph right to h units. ( i i ) Replacing x by x + h , shift the graph left to h units. ( i i i ) Replacing y by y − k , shift the graph upward to k units. ( i v ) Replacing y by y + k , shift the graph downward to k units.” The given equation of conic is ( y − 2 ) 2 = 4 ( x + 2 ) . Use the definition “The equation of shifted parabola with vertex V ( h , k ) is ( y − k ) 2 = 4 p ( x − h ) ” in the equation of parabola ( y − 2 ) 2 = 4 ( x + 2 ) . Here, h = − 2 and k = 2 . Therefore, by above definition the vertex of the parabola ( y − 2 ) 2 = 4 ( x + 2 ) is V ( − 2 , 2 ) . The equation ( y − 2 ) 2 = 4 ( x + 2 ) is the shifted parabolic equation of y 2 = 4 x . The equation of parabola ( y − 2 ) 2 = 4 ( x + 2 ) may obtain as from the equation of parabola y 2 = 4 x by replacing x by x + 2 and y by y − 2 (b) To determine To sketch: The graph and directrix of the parabola ( y − 2 ) 2 = 4 ( x + 2 ) .

Precalculus: Mathematics for Calculus (Standalone Book)

7th Edition

ISBN: 9781305071759

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Brooks Cole

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Chapter 11, Problem 7RE

(a)

To determine

To find: The vertex, focus and directrix of the parabola (y−2)2=4(x+2) .

(b)

To determine

To sketch: The graph and directrix of the parabola (y−2)2=4(x+2) .

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Chapter 11, Problem 6RE

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Precalculus: Mathematics for Calculus (Standalone Book)

Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 6E Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 8E Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...

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The vertex, focus and directrix of the parabola ( y − 2 ) 2 = 4 ( x + 2 ) .

Solution Summary: The author explains the vertex, focus, and directrix of the parabola.