Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Minimization
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Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
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In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Question
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Chapter 5.2, Problem 36PPS
To determine

To find: the two real numbers with a sum of −13 and a product of 42 by using quadratic equation.

Expert Solution & Answer
Check Mark

Answer to Problem 36PPS

  −7 and −6 .

Explanation of Solution

Given:

The sum of two real number is −13 and its product of 42 .

Calculation:

Represent the given condition is expressed in to standard form:

Let x be the variable for the first unknown number.

And −13−x for the second unknown number.

Therefore, according to the question,

  x(−13−x)=42                   {given equation}−13x−x2=42                     {simplify}−x2−13x−42=0                 {equate one side to 0} .

Now, graph the related quadratic function to show that x-intercept of the graph. Therefore,

  Algebra 2, Chapter 5.2, Problem 36PPS

Looking at the graph, the parabola crosses the x-axis, therefore, the equation has the solution.

The axis of symmetric is

  x=−b2a                                          {equation for symmetry}x=−(−13) 2(−1)                                 {substitutes these value}x=−132=−6.5

Now write the table for the given function.

    x−8−7−6.5−6−5
    f(x)−200.250−2

Based on the table and the graph, the function has two zero −7 and −6 .

Hence, the solution of the given equation is between −7 and −6

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Chapter 5.2, Problem 35PPS
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Chapter 5.2, Problem 37PPS

Chapter 5 Solutions

Algebra 2

Ch. 5.1 - Prob. 1ACYPCh. 5.1 - Prob. 1BCYPCh. 5.1 - Prob. 2ACYPCh. 5.1 - Prob. 2BCYPCh. 5.1 - Prob. 2CCYPCh. 5.1 - Prob. 3ACYPCh. 5.1 - Prob. 3BCYPCh. 5.1 - Prob. 3CCYPCh. 5.1 - Prob. 4CYPCh. 5.1 - Prob. 1CYU
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Prob. 33PPSCh. 5.6 - Prob. 34PPSCh. 5.6 - Prob. 35PPSCh. 5.6 - Prob. 36PPSCh. 5.6 - Prob. 37PPSCh. 5.6 - Prob. 38PPSCh. 5.6 - Prob. 39PPSCh. 5.6 - Prob. 40PPSCh. 5.6 - Prob. 41PPSCh. 5.6 - Prob. 42PPSCh. 5.6 - Prob. 43HPCh. 5.6 - Prob. 44HPCh. 5.6 - Prob. 45HPCh. 5.6 - Prob. 46HPCh. 5.6 - Prob. 47HPCh. 5.6 - Prob. 48HPCh. 5.6 - Prob. 49HPCh. 5.6 - Prob. 50HPCh. 5.6 - Prob. 51HPCh. 5.6 - Prob. 52HPCh. 5.6 - Prob. 53STPCh. 5.6 - Prob. 54STPCh. 5.6 - Prob. 55STPCh. 5.6 - Prob. 56STPCh. 5.6 - Prob. 57STPCh. 5.6 - Prob. 58STPCh. 5.6 - Prob. 59STPCh. 5.6 - Prob. 60STPCh. 5.6 - Prob. 61SCh. 5.6 - Prob. 62SCh. 5.6 - Prob. 63SCh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.7 - Prob. 1ACYPCh. 5.7 - Prob. 1BCYPCh. 5.7 - Prob. 2CYPCh. 5.7 - Prob. 3ACYPCh. 5.7 - Prob. 3BCYPCh. 5.7 - Prob. 1CYUCh. 5.7 - Prob. 2CYUCh. 5.7 - Prob. 3CYUCh. 5.7 - Prob. 4CYUCh. 5.7 - Prob. 5CYUCh. 5.7 - Prob. 6CYUCh. 5.7 - Prob. 7CYUCh. 5.7 - Prob. 8PPSCh. 5.7 - Prob. 9PPSCh. 5.7 - Prob. 10PPSCh. 5.7 - Prob. 11PPSCh. 5.7 - Prob. 12PPSCh. 5.7 - Prob. 13PPSCh. 5.7 - Prob. 14PPSCh. 5.7 - Prob. 15PPSCh. 5.7 - Prob. 16PPSCh. 5.7 - Prob. 17PPSCh. 5.7 - Prob. 18PPSCh. 5.7 - Prob. 19PPSCh. 5.7 - Prob. 20PPSCh. 5.7 - Prob. 21PPSCh. 5.7 - Prob. 22PPSCh. 5.7 - Prob. 23PPSCh. 5.7 - Prob. 24PPSCh. 5.7 - Prob. 25PPSCh. 5.7 - Prob. 26PPSCh. 5.7 - Prob. 27PPSCh. 5.7 - Prob. 28PPSCh. 5.7 - Prob. 29PPSCh. 5.7 - Prob. 30PPSCh. 5.7 - Prob. 31PPSCh. 5.7 - Prob. 32PPSCh. 5.7 - Prob. 33PPSCh. 5.7 - Prob. 34PPSCh. 5.7 - Prob. 35PPSCh. 5.7 - Prob. 36PPSCh. 5.7 - Prob. 37PPSCh. 5.7 - Prob. 38PPSCh. 5.7 - Prob. 39PPSCh. 5.7 - Prob. 40PPSCh. 5.7 - Prob. 41PPSCh. 5.7 - Prob. 42PPSCh. 5.7 - Prob. 43PPSCh. 5.7 - Prob. 44PPSCh. 5.7 - Prob. 45PPSCh. 5.7 - Prob. 46PPSCh. 5.7 - Prob. 47PPSCh. 5.7 - Prob. 48HPCh. 5.7 - Prob. 49HPCh. 5.7 - Prob. 50HPCh. 5.7 - Prob. 51HPCh. 5.7 - Prob. 52HPCh. 5.7 - Prob. 53HPCh. 5.7 - Prob. 54HPCh. 5.7 - Prob. 55HPCh. 5.7 - Prob. 56HPCh. 5.7 - Prob. 57STPCh. 5.7 - Prob. 58STPCh. 5.7 - Prob. 59STPCh. 5.7 - Prob. 60STPCh. 5.7 - Prob. 61STPCh. 5.7 - Prob. 62STPCh. 5.7 - Prob. 63STPCh. 5.7 - Prob. 64STPCh. 5.7 - Prob. 65STPCh. 5.7 - Prob. 66STPCh. 5.7 - Prob. 67STPCh. 5.7 - Prob. 68STPCh. 5.7 - Prob. 69STPCh. 5.7 - Prob. 70STPCh. 5.7 - Prob. 71STPCh. 5.7 - Prob. 72STPCh. 5.7 - Prob. 73STPCh. 5.7 - Prob. 74SCh. 5.7 - Prob. 75SCh. 5.7 - Prob. 76SCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.8 - Prob. 1ACYPCh. 5.8 - Prob. 1BCYPCh. 5.8 - Prob. 2ACYPCh. 5.8 - Prob. 2BCYPCh. 5.8 - Prob. 3ACYPCh. 5.8 - Prob. 3BCYPCh. 5.8 - Prob. 4CYPCh. 5.8 - Prob. 5ACYPCh. 5.8 - Prob. 5BCYPCh. 5.8 - Prob. 1CYUCh. 5.8 - Prob. 2CYUCh. 5.8 - Prob. 3CYUCh. 5.8 - Prob. 4CYUCh. 5.8 - Prob. 5CYUCh. 5.8 - Prob. 6CYUCh. 5.8 - Prob. 7CYUCh. 5.8 - Prob. 8CYUCh. 5.8 - Prob. 9CYUCh. 5.8 - Prob. 10CYUCh. 5.8 - Prob. 11CYUCh. 5.8 - Prob. 12CYUCh. 5.8 - Prob. 13PPSCh. 5.8 - Prob. 14PPSCh. 5.8 - Prob. 15PPSCh. 5.8 - Prob. 16PPSCh. 5.8 - Prob. 17PPSCh. 5.8 - Prob. 18PPSCh. 5.8 - Prob. 19PPSCh. 5.8 - Prob. 20PPSCh. 5.8 - Prob. 21PPSCh. 5.8 - Prob. 22PPSCh. 5.8 - Prob. 23PPSCh. 5.8 - Prob. 24PPSCh. 5.8 - Prob. 25PPSCh. 5.8 - Prob. 26PPSCh. 5.8 - Prob. 27PPSCh. 5.8 - Prob. 28PPSCh. 5.8 - Prob. 29PPSCh. 5.8 - Prob. 30PPSCh. 5.8 - Prob. 31PPSCh. 5.8 - Prob. 32PPSCh. 5.8 - Prob. 33PPSCh. 5.8 - Prob. 34PPSCh. 5.8 - Prob. 35PPSCh. 5.8 - Prob. 36PPSCh. 5.8 - Prob. 37PPSCh. 5.8 - Prob. 38PPSCh. 5.8 - Prob. 39PPSCh. 5.8 - Prob. 40PPSCh. 5.8 - Prob. 41PPSCh. 5.8 - Prob. 42PPSCh. 5.8 - Prob. 43PPSCh. 5.8 - Prob. 44PPSCh. 5.8 - Prob. 45PPSCh. 5.8 - Prob. 46PPSCh. 5.8 - Prob. 47PPSCh. 5.8 - Prob. 48PPSCh. 5.8 - Prob. 49PPSCh. 5.8 - Prob. 50PPSCh. 5.8 - Prob. 51PPSCh. 5.8 - Prob. 52PPSCh. 5.8 - Prob. 53PPSCh. 5.8 - Prob. 54PPSCh. 5.8 - Prob. 55PPSCh. 5.8 - Prob. 56PPSCh. 5.8 - Prob. 57HPCh. 5.8 - Prob. 58HPCh. 5.8 - Prob. 59HPCh. 5.8 - Prob. 60HPCh. 5.8 - Prob. 61HPCh. 5.8 - Prob. 62HPCh. 5.8 - Prob. 63HPCh. 5.8 - Prob. 64HPCh. 5.8 - Prob. 65HPCh. 5.8 - Prob. 66HPCh. 5.8 - Prob. 67STPCh. 5.8 - Prob. 68STPCh. 5.8 - Prob. 69STPCh. 5.8 - Prob. 70STPCh. 5.8 - Prob. 71STPCh. 5.8 - Prob. 72STPCh. 5.8 - Prob. 73STPCh. 5.8 - Prob. 74STPCh. 5.8 - Prob. 75STPCh. 5.8 - Prob. 76STPCh. 5.8 - Prob. 77SCh. 5.8 - Prob. 78SCh. 5.8 - Prob. 79SCh. 5.8 - Prob. 80SCh. 5.8 - Prob. 81SCh. 5.8 - Prob. 82SCh. 5 - Prob. 1QCCh. 5 - Prob. 2QCCh. 5 - Prob. 3QCCh. 5 - Prob. 4QCCh. 5 - Prob. 5QCCh. 5 - Prob. 6QCCh. 5 - Prob. 7QCCh. 5 - Prob. 8QCCh. 5 - Prob. 9QCCh. 5 - Prob. 10QCCh. 5 - Prob. 11QCCh. 5 - Prob. 12QCCh. 5 - Prob. 13QCCh. 5 - Prob. 14QCCh. 5 - Prob. 15QCCh. 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. 20MCQCh. 5 - Prob. 21MCQCh. 5 - Prob. 22MCQCh. 5 - Prob. 23MCQCh. 5 - Prob. 1SGRCh. 5 - Prob. 2SGRCh. 5 - Prob. 3SGRCh. 5 - Prob. 4SGRCh. 5 - Prob. 5SGRCh. 5 - Prob. 6SGRCh. 5 - Prob. 7SGRCh. 5 - Prob. 8SGRCh. 5 - Prob. 9SGRCh. 5 - Prob. 10SGRCh. 5 - Prob. 11SGRCh. 5 - Prob. 12SGRCh. 5 - Prob. 13SGRCh. 5 - Prob. 14SGRCh. 5 - Prob. 15SGRCh. 5 - Prob. 16SGRCh. 5 - Prob. 17SGRCh. 5 - Prob. 18SGRCh. 5 - Prob. 19SGRCh. 5 - Prob. 20SGRCh. 5 - Prob. 21SGRCh. 5 - Prob. 22SGRCh. 5 - Prob. 23SGRCh. 5 - Prob. 24SGRCh. 5 - Prob. 25SGRCh. 5 - Prob. 26SGRCh. 5 - Prob. 27SGRCh. 5 - Prob. 28SGRCh. 5 - Prob. 29SGRCh. 5 - Prob. 30SGRCh. 5 - Prob. 31SGRCh. 5 - Prob. 32SGRCh. 5 - Prob. 33SGRCh. 5 - Prob. 34SGRCh. 5 - Prob. 35SGRCh. 5 - Prob. 36SGRCh. 5 - Prob. 37SGRCh. 5 - Prob. 38SGRCh. 5 - Prob. 39SGRCh. 5 - Prob. 40SGRCh. 5 - Prob. 41SGRCh. 5 - Prob. 42SGRCh. 5 - Prob. 43SGRCh. 5 - Prob. 44SGRCh. 5 - Prob. 45SGRCh. 5 - Prob. 46SGRCh. 5 - Prob. 47SGRCh. 5 - Prob. 48SGRCh. 5 - Prob. 49SGRCh. 5 - Prob. 50SGRCh. 5 - Prob. 51SGRCh. 5 - Prob. 52SGRCh. 5 - Prob. 53SGRCh. 5 - Prob. 54SGRCh. 5 - Prob. 55SGRCh. 5 - Prob. 56SGRCh. 5 - Prob. 57SGRCh. 5 - Prob. 58SGRCh. 5 - Prob. 59SGRCh. 5 - Prob. 60SGRCh. 5 - Prob. 61SGRCh. 5 - Prob. 62SGRCh. 5 - Prob. 63SGRCh. 5 - Prob. 64SGRCh. 5 - Prob. 65SGRCh. 5 - Prob. 66SGRCh. 5 - Prob. 67SGRCh. 5 - Prob. 68SGRCh. 5 - Prob. 69SGRCh. 5 - Prob. 70SGRCh. 5 - Prob. 71SGRCh. 5 - Prob. 72SGRCh. 5 - Prob. 73SGRCh. 5 - Prob. 1PTCh. 5 - Prob. 2PTCh. 5 - Prob. 3PTCh. 5 - Prob. 4PTCh. 5 - Prob. 5PTCh. 5 - Prob. 6PTCh. 5 - Prob. 7PTCh. 5 - Prob. 8PTCh. 5 - Prob. 9PTCh. 5 - Prob. 10PTCh. 5 - Prob. 11PTCh. 5 - Prob. 12PTCh. 5 - Prob. 13PTCh. 5 - Prob. 14PTCh. 5 - Prob. 15PTCh. 5 - Prob. 16PTCh. 5 - Prob. 17PTCh. 5 - Prob. 18PTCh. 5 - Prob. 19PTCh. 5 - Prob. 20PTCh. 5 - Prob. 21PTCh. 5 - Prob. 22PTCh. 5 - Prob. 23PTCh. 5 - Prob. 24PTCh. 5 - Prob. 25PTCh. 5 - Prob. 26PTCh. 5 - Prob. 1ECh. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 1STPCh. 5 - Prob. 2STPCh. 5 - Prob. 3STPCh. 5 - Prob. 4STPCh. 5 - Prob. 5STPCh. 5 - Prob. 6STPCh. 5 - Prob. 7STPCh. 5 - Prob. 8STPCh. 5 - Prob. 9STPCh. 5 - Prob. 10STPCh. 5 - Prob. 11STPCh. 5 - Prob. 12STPCh. 5 - Prob. 13STPCh. 5 - Prob. 14STPCh. 5 - Prob. 15STPCh. 5 - Prob. 16STP

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