Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q. 82 (page 114)

complete the square of each quadratic expression. Then graph each function using the technique of shifting.

f(x)=-2x2-12x-13

Short Answer

Expert verified

The graph of the given equation is

Step by step solution

01

Step 1. Given information

Given expression:

f(x)=-2x2-12x-13

02

Step 2. Write the concept

In order to complete the square, we will add or subtract some numbers in order to simplify it.

03

Step 3. Calculation

Let us take out -2from the given expression therefore,

-2x2-12x-13=-2x2+6x+132Nowwesubtract9fromitf(x)=-2x2+6x+9+132-9=-2(x+3)2+132-9=-2(x+3)2-52

04

Step 4. Graphing using shifting technique

In order to graph the given expression we need to draw the graph of x2i.e.

05

Step 5. Graphing the actual expression

Replace y=f(x)withy=f(x-h)here h=3 therefore,

06

Step 6. Shifting vertically

The function y=f(x)-kwillbeshiftedverticallydownwardbykunitsf(x)=(x+3)2by52units.

Now, the the actual graph will be the reflection of above graph multiplied by 2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

fx=-x3

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.

The intercepts of the equationy=x2-9are

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free