Explanation Given: The equation of parabola is, x 2 = 3 ( x + y ) 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, x 2 = 3 ( x + y ) Convert the above equation into equation of parabola. x 2 = 3 ( x + y ) x 2 − 3 x + 9 4 = 3 y + 9 4 ( x − 3 2 ) 2 = 3 ( y + 3 4 ) ( x − 3 2 ) 2 = 4 ( 3 4 ) ( y + 3 4 ) Compare the equation of the parabola with the standard equation. h = 3 2 p = 3 4 k = − 3 4 Calculate the vertex of the parabola To determine (b) To sketch: The graph of the parabola and its directrix.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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 12.CR, Problem 12E

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.CR, Problem 11E

Chapter 12.CR, Problem 13E

Students have asked these similar questions

Use the quadratic formula to find the zeros of the quadratic equation. Y=3x^2+48x+180

M = log The formula determines the magnitude of an earthquake, where / is the intensity of the earthquake and S is the intensity of a "standard earthquake." How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work.

Now consider equations of the form ×-a=v = √bx + c, where a, b, and c are all positive integers and b>1. (f) Create an equation of this form that has 7 as a solution and an extraneous solution. Give the extraneous solution. (g) What must be true about the value of bx + c to ensure that there is a real number solution to the equation? Explain.

Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

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

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

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