Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In $12-17,$ use a graph to find the solution set of each inequality.$$-x^{2}-3 x+4 \geq 0$$

The solution set is $[-4,1]$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 5

Polynomial Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Campbell University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

02:41

In $12-17,$ use a graph to…

01:08

01:09

02:58

Solve each inequality, and…

03:44

01:44

02:33

Solve the inequality and s…

01:12

Solve each compound inequa…

04:25

Solve each inequality. Gra…

00:59

Okay, So in this exercise, we are given the any equality. X squared minus two X plus three. Oh, no, I'm sorry. It should be. Plus two X minus three is less than zero. And I've already generated the graph of this particular polynomial right here. But just for clarity. We're gonna go ahead and factor anyways. So this factors into X minus one X plus three. And if we were to expand this, we get X squared minus a plus three x minus X minus three Anyways. Okay. So what we are looking for is the region of X values and their corresponding. Why values that satisfy this inequality? So if I were to pick, let's say, um the number negative three, and plug this into this equation. I get negative. Three squared, plus two times negative. Three minus three equals nine minus six. Minus three equals zero. And technically, zero is not strictly less than zero. So I can't include the value Negative three, but I can include any value. Ah, after that. So I'm gonna put an open dot right there to indicate a open interval. Now, if I were to pick any of these remaining X values like, let's say negative to. For example, I do negative two squared plus two times, thank you. Two minus three. He goes for minus four. Minus three equals negative three, which is less than zero. So that means that this value *** too, is going to satisfy our inequality. And I hope it's pretty clear that all of the values from negative three up to positive one are going to satisfy the inequality given here because all their outputs, like all their functional outputs, are below the X axis axis, which means they're less than zero. So our solution region is actually going to be this entire portion of the proble below the X axis, okay?

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

In $12-17,$ use a graph to find the solution set of each inequality.$$

Solve each inequality, and graph the solution set. $$x^{2}-4 x+3 \ge…

Solve each inequality, and graph the solution set. $$4 x^{2}+7 x \ge…

Solve each inequality, and graph the solution set. See Example $3 .$ $$<…

Solve the inequality and sketch the solution on the real number line. Use a …

Solve each compound inequality, if possible. Graph the solution set (if one …

Solve each inequality. Graph each solution.$$x^{3}-4 x \geq 0$$

Solve each compound inequality. Graph the solution set and write it using in…

In $11-38,$ evaluate each expression in the set of real numbers.$$-\…

In $3-6,$ find the coordinates of the ordered pair with the smallest value o…

02:46

In $13-20$ : a. Graph each function. b. Is the function a direct variation? …

03:52

In $19-25,$ express each answer in simplest radical form. Check each answer.…

In $7-10,$ the domain of each function is the set of real numbers. a. Sketch…

In $3-38$ write each expression in simplest form. Variables in the radicand …

08:20

The lengths of the legs of a right triangle in feet are $(3+\sqrt{3})$ and $…

00:46

In $11-38,$ evaluate each expression in the set of real numbers.$$\s…

00:30

In $7-12,$ determine if each graph represents a one-to-one function.

a. Sketch the graph of $y=|x| .$b. Sketch the graph of $y=2|x|$c. Sk…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.