Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q. 22 (page 171)

In Problems 7–22, solve each inequality.

2(2x2-3x)>-9

Short Answer

Expert verified

The inequality is true on the entire real domain.

Step by step solution

01

Step 1. Given Information

The given inequality is2(2x2-3x)>-9.

02

Step 2. Find the intercepts and vertex

  • Rewrite the inequality in standard form.

4x2-6x+9>0

  • There are no real roots of 4x2-6x+9>0, so, there are no x-intercepts of the curve.
  • The value of f(0)=9.
  • So, the y-intercept is (0,9).
  • Find x=-b2ato find the x - coordinate of the vertex of parabola.

x=68

  • The value of f68=274.
  • So, the vertex is 68,274.
03

Step 3. Graph the Parabola

  • Plot the parabola on a graph by using the obtained intercepts and the vertex.

04

Step 4. Find the region above the x-axis

From the graph, it is observed that the entire curve lies above the x-axis.

So, the entire domain of the function is the solution set.

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

If p(x)=-x+6,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.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

xy=f(x)
-2-4
-10
04
18
212

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

The x-coordinate of the vertex of f(x)=ax2+bx+c,a≠0, is ________.

The vertical line passing through the vertex of a parabola is called the ______________.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

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