Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Chapter 9.1, Problem 67PPS

(a)

To determine

The related function for each equation . Complete the first two columns of the table.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given Information:

The table is :

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  1

Calculation:

Writing the related function :

First make the equation with right hand side = 0 and then we get the related function.

    EquationRelated Function
    x2x=12y=x2x12
    x2+8x=9y=x2+8x9
    x2=14x24y=x214x+24
    x2+16x=28y=x2+16x+28

(b)

To determine

To Graph:

Each related function with graphing calculator.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given Information:

From part (a), we have the table for each related function:

    EquationRelated Function
    x2x=12y=x2x12
    x2+8x=9y=x2+8x9
    x2=14x24y=x214x+24
    x2+16x=28y=x2+16x+28

The related functions:

  1. y=x2x12
  2. y=x2+8x9
  3. y=x214x+24
  4. y=x2+16x+28

Graph:

  • Using TI-83 Plus Graphing Calculator , we graph the given related functions:
  • 1)

    • Let Y1 = x2x12

        Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  2

    • Under the ZOOM option , select 6) and adjust the viewing option to standard:
    •   Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  3

    • Use the WINDOW option to adjust the scaling of the graph :
    •   Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  4

    • Use the GRAPH option to view the graph :
    •   Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  5

      Obtain rest of the graphs of the related functions similarly:

    2) Let Y1= x2+8x9 and adjust the scaling of the graph using WINDOW option , then obtain the graph using GRAPH option:

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  6

    3) Let Y1= x214x+24 and adjust the scaling of the graph using WINDOW option , then obtain the graph using GRAPH option:

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  7

    4) Let Y1= x2+16x+28 and adjust the scaling of the graph using WINDOW option , then obtain the graph using GRAPH option:

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  8

    (c)

    To determine

    To Find:

    Use the table feature on your calculator to determine the zeros of each related function. Record the zeroes in the table below . Also record the values of the function one unit less than and one unit more than each zero.

    (c)

    Expert Solution
    Check Mark

    Explanation of Solution

    Given Information:

    The table is :

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  9

    From part (a), the table is :

      EquationRelated FunctionZeroesy-value one less than the value where Y1=0y-value one more than the value where Y1=0
      x2x=12y=x2x12
      x2+8x=9y=x2+8x9
      x2=14x24y=x214x+24
      x2+16x=28y=x2+16x+28

    Calculation:

    1.

    • Let Y1 = x2x12.
    • Use the 2nd [TABLE] option to get the table of values.
    • Use the up and down arrow to locate the values of x where Y1 = 0.
    • Identify the y -values above and below the value where Y1 = 0.
    • Add these values in the table.

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  10

      EquationRelated FunctionZeroesy-value one less than the value where Y1=0y-value one more than the value where Y1=0
      x2x=12y=x2x12-38-6
      4-68

    2.

    • Let Y1 = x2+8x9.
    • Use the 2nd [TABLE] option to get the table of values.
    • Use the up and down arrow to locate the values of x where Y1 = 0.
    • Identify the y -values above and below the value where Y1 = 0.
    • Add these values in the table.

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  11

      EquationRelated FunctionZeroesy-value one less than the value where Y1=0y-value one more than the value where Y1=0
      x2x=12y=x2x12-38-6
      4-68
      x2+8x=9y=x2+8x9-911-9
      1-911

    3.

    • Let Y1 = x214x+24.
    • Use the 2nd [TABLE] option to get the table of values.
    • Use the up and down arrow to locate the values of x where Y1 = 0.
    • Identify the y -values above and below the value where Y1 = 0.
    • Add these values in the table.

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  12

      EquationRelated FunctionZeroesy-value one less than the value where Y1=0y-value one more than the value where Y1=0
      x2x=12y=x2x12-38-6
      4-68
      x2+8x=9y=x2+8x9-911-9
      1-911
      x2=14x24y=x214x+24211-9
      12-911

    4.

    • Let Y1 = x2+16x+28.
    • Use the 2nd [TABLE] option to get the table of values.
    • Use the up and down arrow to locate the values of x where Y1 = 0.
    • Identify the y -values above and below the value where Y1 = 0.
    • Add these values in the table.

      Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 9.1, Problem 67PPS , additional homework tip  13

      EquationRelated FunctionZeroes( x-coordinate where Y1 = 0)y-value one less than the value where Y1=0y-value one more than the value where Y1=0
      x2x=12y=x2x12-38-6
      4-68
      x2+8x=9y=x2+8x9-911-9
      1-911
      x2=14x24y=x214x+24211-9
      12-911
      x2+16x=28y=x2+16x+28-1413-11
      -2-1113

    (d)

    To determine

    To Examine:

    The function values ( y-values) for x-values just before and just after a zero. What happens to the sign of the value before and after a zero?

    (d)

    Expert Solution
    Check Mark

    Answer to Problem 67PPS

    The function values have opposite signs just before and after the zero.

    Explanation of Solution

    Given Information:

    From part (c) , we have the completed table :

      EquationRelated FunctionZeroes( x-coordinate where Y1 = 0)y-value one less than the value where Y1=0y-value one more than the value where Y1=0
      x2x=12y=x2x12-38-6
      4-68
      x2+8x=9y=x2+8x9-911-9
      1-911
      x2=14x24y=x214x+24211-9
      12-911
      x2+16x=28y=x2+16x+28-1413-11
      -2-1113

    Observation:

    From the above table, for the zero x = -3 of function y=x2x12, the y-values just before and after the zero are y = 8 and y = -6.

    Similarly we can observe that the y-values for each zero changes sign just before the zero and after the zero.

    So, the function values have opposite signs just before and after the zero.

    Chapter 9 Solutions

    Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

    Ch. 9.1 - Prob. 6GPCh. 9.1 - Prob. 1CYUCh. 9.1 - Prob. 2CYUCh. 9.1 - Prob. 3CYUCh. 9.1 - Prob. 4CYUCh. 9.1 - Prob. 5CYUCh. 9.1 - Prob. 6CYUCh. 9.1 - Prob. 7CYUCh. 9.1 - Prob. 8CYUCh. 9.1 - Prob. 9CYUCh. 9.1 - Prob. 10CYUCh. 9.1 - Prob. 11CYUCh. 9.1 - Prob. 12CYUCh. 9.1 - Prob. 13CYUCh. 9.1 - Prob. 14CYUCh. 9.1 - Prob. 15CYUCh. 9.1 - Prob. 16CYUCh. 9.1 - Prob. 17CYUCh. 9.1 - Prob. 18CYUCh. 9.1 - Prob. 19CYUCh. 9.1 - Prob. 20CYUCh. 9.1 - Prob. 21CYUCh. 9.1 - Prob. 22PPSCh. 9.1 - Prob. 23PPSCh. 9.1 - Prob. 24PPSCh. 9.1 - Prob. 25PPSCh. 9.1 - Prob. 26PPSCh. 9.1 - Prob. 27PPSCh. 9.1 - Prob. 28PPSCh. 9.1 - Prob. 29PPSCh. 9.1 - Prob. 30PPSCh. 9.1 - Prob. 31PPSCh. 9.1 - Prob. 32PPSCh. 9.1 - Prob. 33PPSCh. 9.1 - Prob. 34PPSCh. 9.1 - Prob. 35PPSCh. 9.1 - Prob. 36PPSCh. 9.1 - Prob. 37PPSCh. 9.1 - Prob. 38PPSCh. 9.1 - Prob. 39PPSCh. 9.1 - Prob. 40PPSCh. 9.1 - Prob. 41PPSCh. 9.1 - Prob. 42PPSCh. 9.1 - Prob. 43PPSCh. 9.1 - Prob. 44PPSCh. 9.1 - Prob. 45PPSCh. 9.1 - Prob. 46PPSCh. 9.1 - Prob. 47PPSCh. 9.1 - 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Prob. 35PPSCh. 9.6 - Prob. 36PPSCh. 9.6 - Prob. 37PPSCh. 9.6 - Prob. 38PPSCh. 9.6 - Prob. 39PPSCh. 9.6 - Prob. 40PPSCh. 9.6 - Prob. 41PPSCh. 9.6 - Prob. 42PPSCh. 9.6 - Prob. 43PPSCh. 9.6 - Prob. 44PPSCh. 9.6 - Prob. 45PPSCh. 9.6 - Prob. 46PPSCh. 9.6 - Prob. 47PPSCh. 9.6 - Prob. 48PPSCh. 9.6 - Prob. 49PPSCh. 9.6 - Prob. 50PPSCh. 9.6 - Prob. 51HPCh. 9.6 - Prob. 52HPCh. 9.6 - Prob. 53HPCh. 9.6 - Prob. 54HPCh. 9.6 - Prob. 55HPCh. 9.6 - Prob. 56HPCh. 9.6 - Prob. 57HPCh. 9.6 - Prob. 58HPCh. 9.6 - Prob. 59PFACh. 9.6 - Prob. 60PFACh. 9.6 - Prob. 61PFACh. 9.6 - Prob. 62PFACh. 9.6 - Prob. 63PFACh. 9.6 - Prob. 64PFACh. 9.7 - Prob. 1GPCh. 9.7 - Prob. 2GPCh. 9.7 - Prob. 3GPCh. 9.7 - Prob. 4GPCh. 9.7 - Prob. 1CYUCh. 9.7 - Prob. 2CYUCh. 9.7 - Prob. 3CYUCh. 9.7 - Prob. 4CYUCh. 9.7 - Prob. 5CYUCh. 9.7 - Prob. 6CYUCh. 9.7 - Prob. 7CYUCh. 9.7 - Prob. 8CYUCh. 9.7 - Prob. 9CYUCh. 9.7 - Prob. 10PPSCh. 9.7 - Prob. 11PPSCh. 9.7 - Prob. 12PPSCh. 9.7 - Prob. 13PPSCh. 9.7 - Prob. 14PPSCh. 9.7 - Prob. 15PPSCh. 9.7 - Prob. 16PPSCh. 9.7 - Prob. 17PPSCh. 9.7 - Prob. 18PPSCh. 9.7 - Prob. 19PPSCh. 9.7 - Prob. 20PPSCh. 9.7 - Prob. 21PPSCh. 9.7 - Prob. 22PPSCh. 9.7 - Prob. 23PPSCh. 9.7 - Prob. 24PPSCh. 9.7 - Prob. 25PPSCh. 9.7 - Prob. 26PPSCh. 9.7 - Prob. 27PPSCh. 9.7 - Prob. 28HPCh. 9.7 - Prob. 29HPCh. 9.7 - Prob. 30HPCh. 9.7 - Prob. 31HPCh. 9.7 - Prob. 32HPCh. 9.7 - Prob. 33HPCh. 9.7 - Prob. 34PFACh. 9.7 - Prob. 35PFACh. 9.7 - Prob. 36PFACh. 9.7 - Prob. 37PFACh. 9.7 - Prob. 38PFACh. 9.7 - Prob. 39PFACh. 9.7 - Prob. 40PFACh. 9.8 - Prob. 1AGPCh. 9.8 - Prob. 1BGPCh. 9.8 - Prob. 2AGPCh. 9.8 - Prob. 2BGPCh. 9.8 - Prob. 3AGPCh. 9.8 - Prob. 3BGPCh. 9.8 - Prob. 4GPCh. 9.8 - Prob. 1CYUCh. 9.8 - Prob. 2CYUCh. 9.8 - Prob. 3CYUCh. 9.8 - Prob. 4CYUCh. 9.8 - Prob. 5CYUCh. 9.8 - Prob. 6CYUCh. 9.8 - Prob. 7CYUCh. 9.8 - Prob. 8CYUCh. 9.8 - Prob. 9CYUCh. 9.8 - Prob. 10CYUCh. 9.8 - Prob. 11CYUCh. 9.8 - Prob. 12CYUCh. 9.8 - Prob. 13CYUCh. 9.8 - Prob. 14PPSCh. 9.8 - Prob. 15PPSCh. 9.8 - Prob. 16PPSCh. 9.8 - Prob. 17PPSCh. 9.8 - Prob. 18PPSCh. 9.8 - Prob. 19PPSCh. 9.8 - Prob. 20PPSCh. 9.8 - Prob. 21PPSCh. 9.8 - Prob. 22PPSCh. 9.8 - Prob. 23PPSCh. 9.8 - Prob. 24PPSCh. 9.8 - Prob. 25PPSCh. 9.8 - Prob. 26PPSCh. 9.8 - Prob. 27PPSCh. 9.8 - Prob. 28PPSCh. 9.8 - Prob. 29PPSCh. 9.8 - Prob. 30PPSCh. 9.8 - Prob. 31HPCh. 9.8 - Prob. 32HPCh. 9.8 - Prob. 33HPCh. 9.8 - Prob. 34HPCh. 9.8 - Prob. 35HPCh. 9.8 - Prob. 36PFACh. 9.8 - Prob. 37PFACh. 9.8 - Prob. 38PFACh. 9.8 - Prob. 39PFACh. 9.8 - Prob. 40PFACh. 9.8 - Prob. 41PFACh. 9.9 - Prob. 1AGPCh. 9.9 - Prob. 1BGPCh. 9.9 - Prob. 2AGPCh. 9.9 - Prob. 2BGPCh. 9.9 - Prob. 3AGPCh. 9.9 - Prob. 3BGPCh. 9.9 - Prob. 3CGPCh. 9.9 - Prob. 4AGPCh. 9.9 - Prob. 4BGPCh. 9.9 - Prob. 1CYUCh. 9.9 - Prob. 2CYUCh. 9.9 - Prob. 3CYUCh. 9.9 - Prob. 4CYUCh. 9.9 - Prob. 5CYUCh. 9.9 - Prob. 6CYUCh. 9.9 - Prob. 7CYUCh. 9.9 - Prob. 8CYUCh. 9.9 - Prob. 9CYUCh. 9.9 - Prob. 10CYUCh. 9.9 - Prob. 11CYUCh. 9.9 - Prob. 12PPSCh. 9.9 - Prob. 13PPSCh. 9.9 - Prob. 14PPSCh. 9.9 - Prob. 15PPSCh. 9.9 - Prob. 16PPSCh. 9.9 - Prob. 17PPSCh. 9.9 - Prob. 18PPSCh. 9.9 - Prob. 19PPSCh. 9.9 - Prob. 20PPSCh. 9.9 - Prob. 21PPSCh. 9.9 - Prob. 22PPSCh. 9.9 - Prob. 23PPSCh. 9.9 - Prob. 24PPSCh. 9.9 - Prob. 25PPSCh. 9.9 - Prob. 26PPSCh. 9.9 - Prob. 27PPSCh. 9.9 - Prob. 28PPSCh. 9.9 - Prob. 29PPSCh. 9.9 - Prob. 30PPSCh. 9.9 - Prob. 31PPSCh. 9.9 - Prob. 32PPSCh. 9.9 - Prob. 33PPSCh. 9.9 - Prob. 34PPSCh. 9.9 - Prob. 35PPSCh. 9.9 - Prob. 36PPSCh. 9.9 - Prob. 37PPSCh. 9.9 - Prob. 38PPSCh. 9.9 - Prob. 39PPSCh. 9.9 - Prob. 40PPSCh. 9.9 - Prob. 41PPSCh. 9.9 - Prob. 42PPSCh. 9.9 - Prob. 43PPSCh. 9.9 - Prob. 44PPSCh. 9.9 - Prob. 45PPSCh. 9.9 - Prob. 46PPSCh. 9.9 - Prob. 47PPSCh. 9.9 - Prob. 48HPCh. 9.9 - Prob. 49HPCh. 9.9 - Prob. 50HPCh. 9.9 - Prob. 51HPCh. 9.9 - Prob. 52HPCh. 9.9 - Prob. 53PFACh. 9.9 - Prob. 54PFACh. 9.9 - Prob. 55PFACh. 9.9 - Prob. 56PFACh. 9.9 - Prob. 57PFACh. 9.9 - Prob. 58PFACh. 9.9 - Prob. 59PFACh. 9 - Prob. 1MCQCh. 9 - Prob. 2MCQCh. 9 - Prob. 3MCQCh. 9 - Prob. 4MCQCh. 9 - Prob. 5MCQCh. 9 - Prob. 6MCQCh. 9 - Prob. 7MCQCh. 9 - Prob. 8MCQCh. 9 - Prob. 9MCQCh. 9 - Prob. 10MCQCh. 9 - Prob. 11MCQCh. 9 - Prob. 12MCQCh. 9 - Prob. 13MCQCh. 9 - Prob. 14MCQCh. 9 - Prob. 15MCQCh. 9 - Prob. 16MCQCh. 9 - Prob. 17MCQCh. 9 - Prob. 18MCQCh. 9 - Prob. 19MCQCh. 9 - Prob. 20MCQCh. 9 - Prob. 21MCQCh. 9 - Prob. 22MCQCh. 9 - Prob. 23MCQCh. 9 - Prob. 24MCQCh. 9 - Prob. 25MCQCh. 9 - Prob. 26MCQCh. 9 - Prob. 27MCQCh. 9 - Prob. 1SGRCh. 9 - Prob. 2SGRCh. 9 - Prob. 3SGRCh. 9 - Prob. 4SGRCh. 9 - Prob. 5SGRCh. 9 - Prob. 6SGRCh. 9 - Prob. 7SGRCh. 9 - Prob. 8SGRCh. 9 - Prob. 9SGRCh. 9 - Prob. 10SGRCh. 9 - Prob. 11SGRCh. 9 - Prob. 12SGRCh. 9 - Prob. 13SGRCh. 9 - Prob. 14SGRCh. 9 - Prob. 15SGRCh. 9 - Prob. 16SGRCh. 9 - Prob. 17SGRCh. 9 - Prob. 18SGRCh. 9 - Prob. 19SGRCh. 9 - Prob. 20SGRCh. 9 - Prob. 21SGRCh. 9 - Prob. 22SGRCh. 9 - Prob. 23SGRCh. 9 - Prob. 24SGRCh. 9 - Prob. 25SGRCh. 9 - Prob. 26SGRCh. 9 - Prob. 27SGRCh. 9 - Prob. 28SGRCh. 9 - Prob. 29SGRCh. 9 - Prob. 30SGRCh. 9 - Prob. 31SGRCh. 9 - Prob. 32SGRCh. 9 - Prob. 33SGRCh. 9 - Prob. 34SGRCh. 9 - Prob. 35SGRCh. 9 - Prob. 36SGRCh. 9 - Prob. 37SGRCh. 9 - Prob. 38SGRCh. 9 - Prob. 39SGRCh. 9 - Prob. 40SGRCh. 9 - Prob. 41SGRCh. 9 - Prob. 42SGRCh. 9 - Prob. 43SGRCh. 9 - Prob. 44SGRCh. 9 - Prob. 45SGRCh. 9 - Prob. 46SGRCh. 9 - Prob. 47SGRCh. 9 - Prob. 48SGRCh. 9 - Prob. 49SGRCh. 9 - Prob. 50SGRCh. 9 - Prob. 51SGRCh. 9 - Prob. 52SGRCh. 9 - Prob. 53SGRCh. 9 - Prob. 54SGRCh. 9 - Prob. 55SGRCh. 9 - Prob. 56SGRCh. 9 - Prob. 57SGRCh. 9 - Prob. 58SGRCh. 9 - Prob. 59SGRCh. 9 - Prob. 60SGRCh. 9 - Prob. 61SGRCh. 9 - Prob. 62SGRCh. 9 - Prob. 63SGRCh. 9 - Prob. 64SGRCh. 9 - Prob. 65SGRCh. 9 - Prob. 66SGRCh. 9 - Prob. 67SGRCh. 9 - Prob. 68SGRCh. 9 - Prob. 69SGRCh. 9 - Prob. 70SGRCh. 9 - Prob. 71SGRCh. 9 - Prob. 1PTCh. 9 - Prob. 2PTCh. 9 - Prob. 3PTCh. 9 - Prob. 4PTCh. 9 - Prob. 5PTCh. 9 - Prob. 6PTCh. 9 - Prob. 7PTCh. 9 - Prob. 8PTCh. 9 - Prob. 9PTCh. 9 - Prob. 10PTCh. 9 - Prob. 11PTCh. 9 - Prob. 12PTCh. 9 - Prob. 13PTCh. 9 - Prob. 14PTCh. 9 - Prob. 15PTCh. 9 - Prob. 16PTCh. 9 - Prob. 17PTCh. 9 - Prob. 18PTCh. 9 - Prob. 19PTCh. 9 - Prob. 20PTCh. 9 - Prob. 21PTCh. 9 - Prob. 22PTCh. 9 - Prob. 23PTCh. 9 - Prob. 24PTCh. 9 - Prob. 25PTCh. 9 - Prob. 26PTCh. 9 - Prob. 27PTCh. 9 - Prob. 28PTCh. 9 - Prob. 29PTCh. 9 - Prob. 1PFACh. 9 - Prob. 2PFACh. 9 - Prob. 3PFACh. 9 - Prob. 4PFACh. 9 - Prob. 5PFACh. 9 - Prob. 6PFACh. 9 - Prob. 7PFACh. 9 - Prob. 8PFACh. 9 - Prob. 9PFACh. 9 - Prob. 10PFACh. 9 - Prob. 11PFACh. 9 - Prob. 12PFACh. 9 - Prob. 13PFA
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