/*! 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. 18 In problems 7-22, solve the ineq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 18 (page 171)

In problems 7-22, solve the inequality.

x2+2x+4>0

Short Answer

Expert verified

The given inequality has no solution.

Step by step solution

01

Step 1. Given information

The given inequality isx2+2x+4>0

02

Step 2. Find the intercepts and vertex

  • The value of f(0)=4.
  • So, the y-intercept is (0,4).
  • There are no real roots of x2+2x+4=0, so, there are no x-intercepts of the curve.
  • The vertex of the parabola exists at -b2a=-22(1)=-1.
  • Find the value of the function at x=-1.

f(-1)=(-1)2+2(-1)+4=1-2+4=3

  • So, the vertex is (-1,3).
03

Step 3. Plot the graph

Plot the parabola on a graph using the vertex and intercepts calculated in the previous step.

04

Step 4. Find the solution set

  • From the graph, there is no region that lies below the x-axis.
  • So, the given inequality has no solution.

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

True or False The graph of the function f(x)=x2is increasing on the interval(0,鈭�).

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)=23x2+43x-1

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)=3x2+6x

Match each graph to one the following functions.

f(x)=-x2-1

Make up a quadratic function that opens down and has only one x-intercept. Compare yours with others in the class. What are the similarities? What are the differences?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.