   Chapter 10.5, Problem 6E

Chapter
Section
Textbook Problem

# Find the vertex, focus, and directrix of the parabola and sketch its graph.6. (y − 2)2 = 2x + 1

To determine

To Find: The vertex, focus, and directrix of the parabola for the equation (y2)2=2x+1.

Explanation

Given:

The parabola equation is as follows.

(y2)2=2x+1

Rewrite the equation.

(y2)2=2x+112(y2)2=12(x+12)

Calculation:

Compute the vertex of the parabola.

The equation of the vertex is given by

(yk)2=4p(xh)12(y2)2=12(x+12)

Then, the vertex is said to be (h,k).

Therefore, the vertex is (12,2).

Compute the focus of the parabola.

Compare the parabola equation with the below equation,

y2=4px

Take parabola equation as below.

12(y2)2=12(x+12)14p=121=2pp=12

The focus of the parabola can be said as below

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find the derivative of the function. F(x)=x1t+sintdt

Single Variable Calculus: Early Transcendentals, Volume I

#### In Problems 47-50, rationalize the denominator of each fraction and simplify. 50.

Mathematical Applications for the Management, Life, and Social Sciences

#### Divide: 35a3b4c663a3b2c8

Elementary Technical Mathematics

#### Maximize Subject to P=3x4y x+y45x2y10x0,y0

Finite Mathematics for the Managerial, Life, and Social Sciences

#### The graph of x = 2 + 3t, y = 4 − t is a: circle ellipse line parabola

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

#### What is a ceiling effect, and how can it be a problem?

Research Methods for the Behavioral Sciences (MindTap Course List) 