   Chapter 12.4, Problem 15E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS13-20 ■ Graphing Shifted Parabolas An equation of a parabola is given.(a) Find the vertex, focus, and directrix of the parabola. (b) Sketch a graph showing the parabola and its directrix. ( y + 5 ) 2 = − 6 x + 12

To determine

(a)

To find:

The vertex, focus, and directrix of the parabola.

Explanation

Given:

The equation of parabola is,

(y+5)2=6x+12

Approach:

The following equation is the basic equation for an parabola that is not centered at the origin.

(xh)2=4p(yk) or (yk)2=4p(xh)

With the following properties,

Vertex V=(h,k) ……(1)

Focus F=(h,pk) or F=(ph,k) ……(2)

Directrix y=pk or x=ph ……(3)

Calculation:

Consider the equation,

(y+5)2=6x+12

Convert the above equation into equation of parabola.

(y+5)2=(4)4(6)(x2)(y+5)2=4(32)(x2)

Compare the equation of the parabola with the standard equation.

h=2p=(32)k=5

Calculate the vertex of the parabola

To determine

(b)

To sketch:

The graph of the parabola and its directrix.

### 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 