Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
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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Chapter 3.4, Problem 73E
To determine

To prove: That the mean of the solutions is b2a . Also, determine the relation of the fact to the symmetry of the graph of y=ax2+bx+c .

Expert Solution & Answer
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Answer to Problem 73E

The mean of the solutions is b2a and the mean of the solutions and the symmetry are equal.

Explanation of Solution

Given information:

The quadratic equation: ax2+bx+c=0

Calculation:

The given quadratic equation is ax2+bx+c=0 .

Consider the solutions of the given equation are x1 and x2 that is,

  x1=bb24ac2a and x2=b+b24ac2a .

The mean of the above solutions is,

  x1+x22=bb24ac2a+b+b24ac2a2x1+x22=bb24acb+b24ac2a2x1+x22=bb24acb+b24ac2a2x1+x22=2b2a2

Simplify the above expression further.

  x1+x22=2b2a2=b2a

Rewrite the given equation in the vertex form as:

  y=a(x2+bax)+cy+a(ba2)2=a(x2+bax+(ba2)2)y=a(x+b2a)2+4ac4ab24ay=a(x+b2a)2+4acb24a

The symmetry of the graph is x=h ; this means the symmetry of the given equation is x=b2a

Hence, the mean of the solutions is b2a and the mean of the solutions and the symmetry are equal.

Chapter 3 Solutions

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

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - 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