/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 54. Determine without graphing wheth... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q 54. (page 156)

Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.

fx=-2x2+12x

Short Answer

Expert verified

The maximum value is18.

Step by step solution

01

Step 1. Given information.

The given quadratic function isfx=-2x2+12x.

02

Step 2. Determine whether the graph of the function opens up or down.

Compare the given quadratic function fx=-2x2+12xwith fx=ax2+bx+c.

So, role="math" a=-2,b=12,c=0.

If a=-2<0, the parabola opens down, which means that the function has a maximum value and it is the vertex.

03

Step 3. Determine the minimum value.

The maximum value occurs at x=-b2a.

role="math" x=-122-2鈰�鈰�a=-2,b=12=3

The maximum value is:

fx=-2x2+12xf3=-232+123=-18+36=18

04

Step 4. Simplified answer.

Hence, the required maximum value is18.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Determine the quadratic function whose graph is given.

If the slope m of the graph of a linear function is________, the function is increasing over its domain.

Match each graph to one the following functions.

f(x)=x2-1

A is used to help us to see the type of relation, if any, that may exist between two variables.

True or False The graph of f(x)=2x2+3x-4opens up.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.