/*! 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 55. Determine without graphing wheth... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q 55. (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-3

Short Answer

Expert verified

The minimum value is-21.

Step by step solution

01

Step 1. Given information.

The given quadratic function isfx=2x2+12x-3.

02

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

Compare the given quadratic function fx=2x2+12x-3with fx=ax2+bx+c.

So, here a=2,b=12,c=-3.

Ifa=2>0, the parabola opens up, which means that the function has a minimum value and it is the vertex.

03

Step 3. Determine the minimum value.

The minimum value occurs at x=-b2a.

x=-122脳2=-3

The required minimum value is:

fx=2x2+12x-3f-3=2-32+12-3-3=18-36-3=18-39=-21

04

Step 4. Simplified answer.

Hence, the required minimum value is-21.

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

In Problems 7鈥�22, solve each inequality.

2(2x2-3x)>-9

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=12x2+x-1

True or False If the discriminant b2-4ac=0, the graph of f(x)=ax2+bx+c,a鈮�0, will touch the x-axis at its vertex.

Why does the graph of a quadratic function open up if a>0and down if a<0?

If G(x)=-2,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.