Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 3.6, Problem 3E

To determine

To determine: The inequality that matches with its graph with explanation.

Expert Solution & Answer

Answer to Problem 3E

The inequality matches with the graph C.

Explanation of Solution

Given information:

The inequality: y≤x2+4x+3

The graphs:

A. Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 3.6, Problem 3E , additional homework tip 1

B. Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 3.6, Problem 3E , additional homework tip 2

C. Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 3.6, Problem 3E , additional homework tip 3

D. Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 3.6, Problem 3E , additional homework tip 4

Calculation:

The given inequality is y≤x2+4x+3 .

The parabola of the equivalent equation of the inequality has a positive leading coefficient which opens up. So, the inequality does not match with the graph A.

Find the zeros of the equivalent equation x2+4x+3=0 .

To find the zeros of the above equation, factorize the equation.

x2+4x+3=0x2+3x+x+3=0x(x+3)+1(x+3)=0(x+3)(x+1)=0

Solve the above factors for x

x+3=0x=−3

And, x+1=0x=−1

Since, the zeros of the parabola are −1 and −3 .

So, the inequality does not match with the graph B.

Now, take an arbitrary point O(0,0) to check whether the given inequality holds or not.

Substitute 0 for y and 0 for x in the given inequality.

0≤(0)2+4(0)+30≤0+0+30≤3

Hence, the inequality matches with the graph C.

Chapter 3.6, Problem 2E

Chapter 3.6, Problem 4E

Chapter 3 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

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