(a) Explanation The given equation of family of parabola x 2 = 4 p ( y + p ) (1) When p = − 2 , the equation (1) becomes x 2 = − 8 ( y − 2 ) . Use online graphing calculator and draw the graph of the parabola x 2 = − 8 ( y − 2 ) as shown below in Figure 1. From Figure 1, it is observed that the focus of parabola x 2 = − 8 ( y − 2 ) is F ( 0 , 0 ) . When p = − 3 2 , the equation (1) becomes x 2 = − 6 ( y − 3 2 ) . Use online graphing calculator and draw the graph of the parabola x 2 = − 6 ( y − 3 2 ) as shown below in Figure 2. From Figure 2, it is observed that the focus of parabola x 2 = − 6 ( y − 3 2 ) is F ( 0 , 0 ) . When p = − 1 , the equation (1) becomes x 2 = − 4 ( y − 1 ) . Use online graphing calculator and draw the graph of the parabola x 2 = − 4 ( y − 1 ) as shown below in Figure 3. From Figure 3, it is observed that the focus of parabola x 2 = − 4 ( y − 1 ) is F ( 0 , 0 ) . When p = − 1 2 , the equation (1) becomes x 2 = − 2 ( y − 1 2 ) . Use online graphing calculator and draw the graph of the parabola x 2 = − 2 ( y − 1 2 ) as shown below in Figure 4. From Figure 4, it is observed that the focus of parabola x 2 = − 2 ( y − 1 2 ) is F ( 0 , 0 ) . When p = 1 2 , the equation (1) becomes x 2 = 2 ( y + 1 2 ) . Use online graphing calculator and draw the graph of the parabola x 2 = 2 ( y + 1 2 ) as shown below in Figure 5. From Figure 5, it is observed that the focus of parabola x 2 = 2 ( y + 1 2 ) is F ( 0 , 0 ) . When p = 1 , the equation (1) becomes x 2 = 4 ( y + 1 ) . Use online graphing calculator and draw the graph of the parabola x 2 = 4 ( y + 1 ) as shown below in Figure 6. From Figure 6, it is observed that the focus of parabola x 2 = 4 ( y + 1 ) is F ( 0 , 0 ) . When p = 3 2 , the equation (1) becomes x 2 = 6 ( y + 3 2 ) (b) To determine To show: That each parabola of the family x 2 = 4 p ( y + p ) has its focus at origin. (c) To determine To describe: The effect on the graph of moving the vertex closer to the origin.

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 11.4, Problem 65E

(a)

To determine

To draw: The graphs of the family of parabolas x2=4p(y+p) for p=−2,−32,−1,−12,12,1,32 and 2 .

(b)

To determine

To show: That each parabola of the family x2=4p(y+p) has its focus at origin.

(c)

To determine

To describe: The effect on the graph of moving the vertex closer to the origin.

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Chapter 11.4, Problem 64E

Chapter 11.4, Problem 66E

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Chapter 11 Solutions

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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To draw: The graphs of the family of parabolas x 2 = 4 p ( y + p ) for p = − 2 , − 3 2 , − 1 , − 1 2 , 1 2 , 1 , 3 2 and 2 .

Solution Summary: The author illustrates the graphs of the family of parabolas x2=4p(y+p

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To draw: The graphs of the family of parabolas x2=4p(y+p) for p=−2,−32,−1,−12,12,1,32 and 2 .

To show: That each parabola of the family x2=4p(y+p) has its focus at origin.

To describe: The effect on the graph of moving the vertex closer to the origin.

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Chapter 11 Solutions