High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
15th Edition
ISBN: 9780133281163
Author: Prentice Hall
Publisher: Prentice Hall
Expert Solution & Answer
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Chapter 5.1, Problem 33PPSE
Solution

To Describe: The shape of the graph of each cubic function including end behaviour, turning points, and increasing/decreasing intervals.

The graph's end behaviour is rises to the left and falls to the right.

There are 2 turning points:

Increasing on: −2+13927,−2−13927

Decreasing on: −∞,−2+13927,−2−13927,∞

Given:

  y=−9x3−2x2+5x+3

Explanation:

Given the function y=−9x3−2x2+5x+3

To create a table of values, substitute values to the equation.

Substitute x=−1 in y=−9x3−2x2+5x+3 :

  y=−9x3−2x2+5x+3=−9−13−2−12+5−1+3=9−2−5+3=5

Substitute x=−0.5 in y=−9x3−2x2+5x+3 :

  y=−9x3−2x2+5x+3=−9−0.53−2−0.52+5−0.5+3=1.125−0.5−2.5+3=1.125

Substitute x=0 in y=−9x3−2x2+5x+3 :

  y=−9x3−2x2+5x+3=−903−202+50+3=3

Substitute x=0.5 in y=−9x3−2x2+5x+3 :

  y=−9x3−2x2+5x+3=−90.53−20.52+50.5+3=−1.125-0.5+2.5+3=3.875

Substitute x=0.5 in y=−9x3−2x2+5x+3 :

  y=−9x3−2x2+5x+3=−913−212+51+3=−9−2+8=−3

    xy
    −15
    −0.51.125
    03
    0.53.875
    1−3

Graph of the function is as:

  High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11, Chapter 5.1, Problem 33PPSE

Find the end behaviour of y=−9x3−2x2+5x+3 :

The leading coefficient in a polynomial is the coefficient of the leading term which is −9 .

Since the degree is odd, the ends of the function will point in the opposite directions.

Since the leading coefficient is negative, the graph falls to the right.

The graph's end behaviour is rises to the left and falls to the right.

To find the turning points, set y′x=0

  y=−9x3−2x2+5x+3y′=−27x2−4x+5

Set the equation to 0 :

  −27x2−4x+5=0

Use the quadratic formula to find the solutions.

  −b±b2−4ac2a

Substitute the values a=−27,b=−4 , and c=5 into the quadratic formula and solve for x

  =4±−42−4⋅−27⋅52×−27x=−2±13927x=−0.51,0.36

Thus, there are 2 turning points.

Determine the interval of increasing/decreasing:

By using the graph, the graph is

Increasing on: −2+13927,−2−13927

Decreasing on: −∞,−2+13927,−2−13927,∞

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Chapter 5.1, Problem 32PPSE
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Chapter 5.1, Problem 34PPSE

Chapter 5 Solutions

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

Ch. 5.1 - Prob. 1LCCh. 5.1 - Prob. 2LCCh. 5.1 - Prob. 3LCCh. 5.1 - Prob. 4LCCh. 5.1 - Prob. 5LCCh. 5.1 - Prob. 6LCCh. 5.1 - Prob. 7LCCh. 5.1 - Prob. 8PPSECh. 5.1 - Prob. 9PPSECh. 5.1 - Prob. 10PPSE
Ch. 5.1 - Prob. 11PPSECh. 5.1 - Prob. 12PPSECh. 5.1 - Prob. 13PPSECh. 5.1 - Prob. 14PPSECh. 5.1 - Prob. 15PPSECh. 5.1 - Prob. 16PPSECh. 5.1 - Prob. 17PPSECh. 5.1 - Prob. 18PPSECh. 5.1 - Prob. 19PPSECh. 5.1 - Prob. 20PPSECh. 5.1 - Prob. 21PPSECh. 5.1 - Prob. 22PPSECh. 5.1 - Prob. 23PPSECh. 5.1 - Prob. 24PPSECh. 5.1 - Prob. 25PPSECh. 5.1 - Prob. 26PPSECh. 5.1 - Prob. 27PPSECh. 5.1 - Prob. 28PPSECh. 5.1 - Prob. 29PPSECh. 5.1 - Prob. 30PPSECh. 5.1 - Prob. 31PPSECh. 5.1 - Prob. 32PPSECh. 5.1 - Prob. 33PPSECh. 5.1 - Prob. 34PPSECh. 5.1 - Prob. 35PPSECh. 5.1 - Prob. 36PPSECh. 5.1 - Prob. 37PPSECh. 5.1 - Prob. 38PPSECh. 5.1 - Prob. 39PPSECh. 5.1 - Prob. 40PPSECh. 5.1 - Prob. 41PPSECh. 5.1 - Prob. 42PPSECh. 5.1 - Prob. 43PPSECh. 5.1 - Prob. 44PPSECh. 5.1 - Prob. 45PPSECh. 5.1 - Prob. 46PPSECh. 5.1 - Prob. 47PPSECh. 5.1 - Prob. 48PPSECh. 5.1 - Prob. 49PPSECh. 5.1 - Prob. 50PPSECh. 5.1 - Prob. 51PPSECh. 5.1 - Prob. 52PPSECh. 5.1 - Prob. 53PPSECh. 5.1 - Prob. 54PPSECh. 5.1 - Prob. 55PPSECh. 5.1 - Prob. 56PPSECh. 5.1 - Prob. 57PPSECh. 5.2 - Prob. 1LCCh. 5.2 - Prob. 2LCCh. 5.2 - Prob. 3LCCh. 5.2 - Prob. 4LCCh. 5.2 - Prob. 5LCCh. 5.2 - Prob. 6LCCh. 5.2 - Prob. 7PPSECh. 5.2 - Prob. 8PPSECh. 5.2 - Prob. 9PPSECh. 5.2 - Prob. 10PPSECh. 5.2 - Prob. 11PPSECh. 5.2 - Prob. 12PPSECh. 5.2 - Prob. 13PPSECh. 5.2 - Prob. 14PPSECh. 5.2 - Prob. 15PPSECh. 5.2 - Prob. 16PPSECh. 5.2 - Prob. 17PPSECh. 5.2 - Prob. 18PPSECh. 5.2 - Prob. 19PPSECh. 5.2 - Prob. 20PPSECh. 5.2 - Prob. 21PPSECh. 5.2 - Prob. 22PPSECh. 5.2 - Prob. 23PPSECh. 5.2 - Prob. 24PPSECh. 5.2 - Prob. 25PPSECh. 5.2 - Prob. 26PPSECh. 5.2 - Prob. 27PPSECh. 5.2 - Prob. 28PPSECh. 5.2 - Prob. 29PPSECh. 5.2 - Prob. 30PPSECh. 5.2 - Prob. 31PPSECh. 5.2 - Prob. 32PPSECh. 5.2 - Prob. 33PPSECh. 5.2 - Prob. 34PPSECh. 5.2 - Prob. 35PPSECh. 5.2 - Prob. 36PPSECh. 5.2 - Prob. 37PPSECh. 5.2 - Prob. 38PPSECh. 5.2 - Prob. 39PPSECh. 5.2 - Prob. 40PPSECh. 5.2 - Prob. 41PPSECh. 5.2 - Prob. 42PPSECh. 5.2 - Prob. 43PPSECh. 5.2 - Prob. 44PPSECh. 5.2 - Prob. 45PPSECh. 5.2 - 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Prob. 20PPSECh. 5.5 - Prob. 21PPSECh. 5.5 - Prob. 22PPSECh. 5.5 - Prob. 23PPSECh. 5.5 - Prob. 24PPSECh. 5.5 - Prob. 25PPSECh. 5.5 - Prob. 26PPSECh. 5.5 - Prob. 27PPSECh. 5.5 - Prob. 28PPSECh. 5.5 - Prob. 29PPSECh. 5.5 - Prob. 30PPSECh. 5.5 - Prob. 31PPSECh. 5.5 - Prob. 32PPSECh. 5.5 - Prob. 33PPSECh. 5.5 - Prob. 34PPSECh. 5.5 - Prob. 35PPSECh. 5.5 - Prob. 36PPSECh. 5.5 - Prob. 37PPSECh. 5.5 - Prob. 38PPSECh. 5.5 - Prob. 39PPSECh. 5.5 - Prob. 40PPSECh. 5.5 - Prob. 41PPSECh. 5.5 - Prob. 42PPSECh. 5.5 - Prob. 43PPSECh. 5.5 - Prob. 44PPSECh. 5.5 - Prob. 45PPSECh. 5.5 - Prob. 46PPSECh. 5.5 - Prob. 47PPSECh. 5.5 - Prob. 48PPSECh. 5.5 - Prob. 49PPSECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.6 - Prob. 1LCCh. 5.6 - Prob. 2LCCh. 5.6 - Prob. 3LCCh. 5.6 - Prob. 4LCCh. 5.6 - Prob. 5LCCh. 5.6 - Prob. 6LCCh. 5.6 - Prob. 7LCCh. 5.6 - Prob. 8PPSECh. 5.6 - Prob. 9PPSECh. 5.6 - Prob. 10PPSECh. 5.6 - Prob. 11PPSECh. 5.6 - Prob. 12PPSECh. 5.6 - Prob. 13PPSECh. 5.6 - Prob. 14PPSECh. 5.6 - Prob. 15PPSECh. 5.6 - Prob. 16PPSECh. 5.6 - Prob. 17PPSECh. 5.6 - Prob. 18PPSECh. 5.6 - Prob. 19PPSECh. 5.6 - Prob. 20PPSECh. 5.6 - Prob. 21PPSECh. 5.6 - Prob. 22PPSECh. 5.6 - Prob. 23PPSECh. 5.6 - Prob. 24PPSECh. 5.6 - Prob. 25PPSECh. 5.6 - Prob. 26PPSECh. 5.6 - Prob. 27PPSECh. 5.6 - Prob. 28PPSECh. 5.6 - Prob. 29PPSECh. 5.6 - Prob. 30PPSECh. 5.6 - Prob. 31PPSECh. 5.6 - Prob. 32PPSECh. 5.6 - Prob. 33PPSECh. 5.6 - Prob. 34PPSECh. 5.6 - Prob. 35PPSECh. 5.6 - Prob. 36PPSECh. 5.6 - Prob. 37PPSECh. 5.6 - Prob. 38PPSECh. 5.6 - Prob. 39PPSECh. 5.6 - Prob. 40PPSECh. 5.6 - Prob. 41PPSECh. 5.6 - Prob. 42PPSECh. 5.6 - Prob. 43PPSECh. 5.6 - Prob. 44PPSECh. 5.6 - Prob. 45PPSECh. 5.6 - Prob. 46PPSECh. 5.6 - Prob. 47PPSECh. 5.6 - Prob. 48PPSECh. 5.6 - Prob. 49PPSECh. 5.6 - Prob. 50PPSECh. 5.6 - Prob. 51PPSECh. 5.6 - Prob. 52PPSECh. 5.6 - Prob. 53PPSECh. 5.6 - Prob. 54PPSECh. 5.6 - Prob. 55PPSECh. 5.6 - Prob. 56PPSECh. 5.6 - Prob. 57PPSECh. 5.6 - Prob. 58PPSECh. 5.6 - Prob. 59PPSECh. 5.6 - Prob. 60PPSECh. 5.6 - Prob. 61PPSECh. 5.6 - Prob. 62PPSECh. 5.6 - Prob. 63PPSECh. 5.6 - Prob. 64PPSECh. 5.6 - Prob. 65PPSECh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.7 - Prob. 1LCCh. 5.7 - Prob. 2LCCh. 5.7 - Prob. 3LCCh. 5.7 - Prob. 4LCCh. 5.7 - Prob. 5LCCh. 5.7 - Prob. 6LCCh. 5.7 - Prob. 7LCCh. 5.7 - Prob. 8PPSECh. 5.7 - Prob. 9PPSECh. 5.7 - Prob. 10PPSECh. 5.7 - Prob. 11PPSECh. 5.7 - Prob. 12PPSECh. 5.7 - Prob. 13PPSECh. 5.7 - Prob. 14PPSECh. 5.7 - Prob. 15PPSECh. 5.7 - Prob. 16PPSECh. 5.7 - Prob. 17PPSECh. 5.7 - Prob. 18PPSECh. 5.7 - Prob. 19PPSECh. 5.7 - Prob. 20PPSECh. 5.7 - Prob. 21PPSECh. 5.7 - Prob. 22PPSECh. 5.7 - Prob. 23PPSECh. 5.7 - Prob. 24PPSECh. 5.7 - Prob. 25PPSECh. 5.7 - Prob. 26PPSECh. 5.7 - Prob. 27PPSECh. 5.7 - Prob. 28PPSECh. 5.7 - Prob. 29PPSECh. 5.7 - Prob. 30PPSECh. 5.7 - Prob. 31PPSECh. 5.7 - Prob. 32PPSECh. 5.7 - Prob. 33PPSECh. 5.7 - Prob. 34PPSECh. 5.7 - Prob. 35PPSECh. 5.7 - Prob. 36PPSECh. 5.7 - 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Prob. 4LCCh. 5.9 - Prob. 5LCCh. 5.9 - Prob. 6LCCh. 5.9 - Prob. 7PPSECh. 5.9 - Prob. 8PPSECh. 5.9 - Prob. 9PPSECh. 5.9 - Prob. 10PPSECh. 5.9 - Prob. 11PPSECh. 5.9 - Prob. 12PPSECh. 5.9 - Prob. 13PPSECh. 5.9 - Prob. 14PPSECh. 5.9 - Prob. 15PPSECh. 5.9 - Prob. 16PPSECh. 5.9 - Prob. 17PPSECh. 5.9 - Prob. 18PPSECh. 5.9 - Prob. 19PPSECh. 5.9 - Prob. 20PPSECh. 5.9 - Prob. 21PPSECh. 5.9 - Prob. 22PPSECh. 5.9 - Prob. 23PPSECh. 5.9 - Prob. 24PPSECh. 5.9 - Prob. 25PPSECh. 5.9 - Prob. 26PPSECh. 5.9 - Prob. 27PPSECh. 5.9 - Prob. 28PPSECh. 5.9 - Prob. 29PPSECh. 5.9 - Prob. 30PPSECh. 5.9 - Prob. 31PPSECh. 5.9 - Prob. 32PPSECh. 5.9 - Prob. 33PPSECh. 5.9 - Prob. 34PPSECh. 5.9 - Prob. 35PPSECh. 5.9 - Prob. 36PPSECh. 5.9 - Prob. 37PPSECh. 5.9 - Prob. 38PPSECh. 5.9 - Prob. 39PPSECh. 5.9 - Prob. 40PPSECh. 5.9 - Prob. 41PPSECh. 5.9 - Prob. 42PPSECh. 5.9 - Prob. 43PPSECh. 5.9 - Prob. 44PPSECh. 5.9 - Prob. 45PPSECh. 5.9 - Prob. 46PPSECh. 5.9 - Prob. 47PPSECh. 5.9 - Prob. 48PPSECh. 5.9 - Prob. 49PPSECh. 5.9 - Prob. 50PPSECh. 5.9 - Prob. 51PPSECh. 5.9 - Prob. 52PPSECh. 5.9 - Prob. 53PPSECh. 5.9 - Prob. 54PPSECh. 5.9 - Prob. 55PPSECh. 5.9 - Prob. 56PPSECh. 5 - Prob. 1GRCh. 5 - Prob. 2GRCh. 5 - Prob. 3GRCh. 5 - Prob. 4GRCh. 5 - Prob. 5GRCh. 5 - Prob. 6GRCh. 5 - Prob. 7GRCh. 5 - Prob. 8GRCh. 5 - Prob. 9GRCh. 5 - Prob. 10GRCh. 5 - Prob. 11GRCh. 5 - Prob. 12GRCh. 5 - Prob. 13GRCh. 5 - Prob. 14GRCh. 5 - Prob. 15GRCh. 5 - Prob. 16GRCh. 5 - Prob. 17GRCh. 5 - Prob. 18GRCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 1CVCh. 5 - Prob. 2CVCh. 5 - Prob. 3CVCh. 5 - Prob. 4CVCh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 7ECh. 5 - Prob. 8ECh. 5 - Prob. 9ECh. 5 - Prob. 10ECh. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - Prob. 13ECh. 5 - Prob. 14ECh. 5 - Prob. 15ECh. 5 - Prob. 16ECh. 5 - Prob. 17ECh. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Prob. 43ECh. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - Prob. 72ECh. 5 - Prob. 73ECh. 5 - Prob. 74ECh. 5 - Prob. 75ECh. 5 - Prob. 76ECh. 5 - Prob. 77ECh. 5 - Prob. 78ECh. 5 - Prob. 79ECh. 5 - Prob. 80ECh. 5 - Prob. 81ECh. 5 - Prob. 82ECh. 5 - Prob. 83ECh. 5 - Prob. 84ECh. 5 - Prob. 85ECh. 5 - Prob. 86ECh. 5 - Prob. 87ECh. 5 - Prob. 88ECh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 1CCSRCh. 5 - Prob. 2CCSRCh. 5 - Prob. 3CCSRCh. 5 - Prob. 4CCSRCh. 5 - Prob. 5CCSRCh. 5 - Prob. 6CCSRCh. 5 - Prob. 7CCSRCh. 5 - Prob. 8CCSRCh. 5 - Prob. 9CCSRCh. 5 - Prob. 10CCSRCh. 5 - Prob. 11CCSRCh. 5 - Prob. 12CCSRCh. 5 - Prob. 13CCSRCh. 5 - Prob. 14CCSRCh. 5 - Prob. 15CCSRCh. 5 - Prob. 16CCSRCh. 5 - Prob. 17CCSRCh. 5 - Prob. 18CCSRCh. 5 - Prob. 19CCSRCh. 5 - Prob. 20CCSRCh. 5 - Prob. 21CCSRCh. 5 - Prob. 22CCSRCh. 5 - Prob. 23CCSR
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