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 4.5, Problem 13E
To determine

To find: the zeros of the given function. Also sketch the graph of the function.

Expert Solution & Answer
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Answer to Problem 13E

The zeros of the given function is x=0,x=3 and x=2 .

Explanation of Solution

Given information:

A function is given as

  h(x)=x4+x36x2

Concept used:

Leading coefficient of a polynomial function is the coefficient of the leading term.

Degree of the polynomial is the degree of leading term or the height degree in the polynomial function.

For the polynomial f(x)=anxn+an1xn1+...+a1x+a0 the leading coefficient is an and the degree is n .

The end behavior can describe the graph of a polynomial function as  x  approaches + or as  x  approaches .

The end behavior of a polynomial function can be determined by the leading coefficient and the degree of the polynomial.

If degree is even and leading coefficient is negative.

  f(x) as x and f(x) as x+ .

If degree is odd and leading coefficient is negative.

  f(x) as x and f(x) as x+ .

If degree is odd and leading coefficient is positive.

  f(x) as x and f(x) as x+ .

If degree is even and leading coefficient is positive.

  f(x) as x and f(x) as x+ .

Zeros of a polynomial function can be found by equating the function with 0.

Calculation:

Consider the given function.

  h(x)=x4+x36x2

Now, for zeros of the function equate the function with 0.

  h(x)=0x4+x36x2=0

Take common x2 from each term of left side of the equation.

  x2(x2+x6)=0

Now, break the coefficient of middle term 1 as sum or difference of two numbers such that product of the numbers is equal to the product of first term and constant term that is product of 1 and 6 .

Such numbers will be 2 and 3 .

Now, factorize left side of x2(x2+x6)=0 as shown:

  x2(x2+x6)=0x2(x2+3x2x6)=0x2[x(x+3)2(x+3)]=0x2(x+3)(x2)=0

Solution can be found by equating each factor with 0.

  x=0

And

  x+3=0x=3

Further,

  x2=0x=2

Therefore, the zeros of the given function is x=0,x=3 and x=2 .

So, the graph crosses x axis at x=2,x=3,x=0 .

Degree is even and leading coefficient is positive.

  h(x) as x and h(x) as x+ .

Graph:

The graph of the function can be sketched by the characteristics.

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 4.5, Problem 13E

Chapter 4 Solutions

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

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - 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