(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.

7th Edition

ISBN: 9781337431125

Author: Watson

Publisher: CENGAGE LEARNING - CONSIGNMENT

See similar textbooks

Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Videos

Question

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.4, Problem 64E

Chapter 11.4, Problem 66E

Students have asked these similar questions

In each of Problems 1 through 4, draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → ∞. If this behavior depends on the initial value of y at t = 0, describe the dependency.1. y′ = 3 − 2y

B 2- The figure gives four points and some corresponding rays in the xy-plane. Which of the following is true? A B Angle COB is in standard position with initial ray OB and terminal ray OC. Angle COB is in standard position with initial ray OC and terminal ray OB. C Angle DOB is in standard position with initial ray OB and terminal ray OD. D Angle DOB is in standard position with initial ray OD and terminal ray OB.

temperature in degrees Fahrenheit, n hours since midnight. 5. The temperature was recorded at several times during the day. Function T gives the Here is a graph for this function. To 29uis a. Describe the overall trend of temperature throughout the day. temperature (Fahrenheit) 40 50 50 60 60 70 5 10 15 20 25 time of day b. Based on the graph, did the temperature change more quickly between 10:00 a.m. and noon, or between 8:00 p.m. and 10:00 p.m.? Explain how you know. (From Unit 4, Lesson 7.) 6. Explain why this graph does not represent a function. (From Unit 4, Lesson 8.)

Chapter 11 Solutions

EBK PRECALCULUS: MATHEMATICS FOR CALCUL

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...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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

Concept explainers

Videos

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.

Want to see the full answer?

Chapter 11 Solutions