Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

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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 9, Problem 13SGR

(a)

To determine

Define the function y=x2−2x−3 has a minimum or maximum value.

(a)

Expert Solution
Check Mark

Answer to Problem 13SGR

The function y=x2−2x−3 has a minimum value.

Explanation of Solution

Given:

The function y=x2−2x−3

Concept Used:

If the coefficient of x2 is positive, then the graph of the parabola is upward open and vertex is at minimum.

If the coefficient of x2 is negative, then the graph of the parabola is downward open and vertex is at maximum.

The graph of any quadratic function is a parabola.

    y=ax2+bx+c(a is positive) − minimum y=−  ax2+bx+c(a is negative) − maximum
    Algebra 1, Chapter 9, Problem 13SGR , additional homework tip 1Algebra 1, Chapter 9, Problem 13SGR , additional homework tip 2

Thus, the function y=x2−2x−3 has a minimum value.

(b)

To determine

State the maximum or minimum value

(b)

Expert Solution
Check Mark

Answer to Problem 13SGR

Manimum value is at x = 1

Explanation of Solution

Given: The function y=x2−2x−3

Concept Used:

If the coefficient of x2 is positive, then the graph of the parabola is upward open and vertex is at minimum.

If the coefficient of x2 is negative, then the graph of the parabola is downward open and vertex is at maximum.

The graph of any quadratic function is a parabola.

    y=ax2+bx+c(a is positive) − minimum y=−  ax2+bx+c(a is negative) − maximum
    Algebra 1, Chapter 9, Problem 13SGR , additional homework tip 3Algebra 1, Chapter 9, Problem 13SGR , additional homework tip 4

Calculation: The graph of the function y=x2−2x−3

  Algebra 1, Chapter 9, Problem 13SGR , additional homework tip 5

Thus, the graph has minimum value is at x = 1

(c)

To determine

Find the domain and range of the function.

(c)

Expert Solution
Check Mark

Answer to Problem 13SGR

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or {y|y≥4}

Explanation of Solution

Given: The function: y=x2−2x−3

Concept Used:

The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible x-values which will make the function "work", and will output real y-values. 

The range of a function is the complete set of all possible resulting values of the dependent variable ( y,  usually), after we have substituted the domain.

Thus, the domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or {y|y≥4}

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Chapter 9, Problem 12SGR
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Chapter 9, Problem 14SGR

Chapter 9 Solutions

Algebra 1

Ch. 9.1 - Prob. 67PPSCh. 9.1 - Prob. 68HPCh. 9.1 - Prob. 69HPCh. 9.1 - Prob. 70HPCh. 9.1 - Prob. 71HPCh. 9.1 - Prob. 72HPCh. 9.1 - Prob. 73HPCh. 9.1 - Prob. 74HPCh. 9.1 - Prob. 75STPCh. 9.1 - Prob. 76STP
Ch. 9.1 - Prob. 77STPCh. 9.1 - Prob. 78STPCh. 9.1 - Prob. 79SRCh. 9.1 - Prob. 80SRCh. 9.1 - Prob. 81SRCh. 9.1 - Prob. 82SRCh. 9.1 - Prob. 83SRCh. 9.1 - Prob. 84SRCh. 9.1 - Prob. 85SRCh. 9.1 - Prob. 86SRCh. 9.1 - Prob. 87SRCh. 9.1 - Prob. 88SRCh. 9.1 - Prob. 89SRCh. 9.1 - Prob. 90SRCh. 9.1 - Prob. 91SRCh. 9.1 - Prob. 92SRCh. 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 - Prob. 48PPSCh. 9.1 - Prob. 49PPSCh. 9.1 - Prob. 50PPSCh. 9.1 - Prob. 51PPSCh. 9.1 - Prob. 52PPSCh. 9.1 - Prob. 53PPSCh. 9.1 - Prob. 54PPSCh. 9.1 - Prob. 55PPSCh. 9.1 - Prob. 56PPSCh. 9.1 - Prob. 57PPSCh. 9.1 - Prob. 58PPSCh. 9.1 - Prob. 59PPSCh. 9.1 - Prob. 60PPSCh. 9.1 - Prob. 61PPSCh. 9.1 - Prob. 62PPSCh. 9.1 - Prob. 63PPSCh. 9.1 - Prob. 64PPSCh. 9.1 - Prob. 65PPSCh. 9.1 - Prob. 66PPSCh. 9.1 - Prob. 93SCh. 9.1 - Prob. 94SCh. 9.1 - Prob. 95SCh. 9.1 - Prob. 1CYPCh. 9.1 - 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Prob. 6CYUCh. 9.3 - Prob. 7CYUCh. 9.3 - Prob. 8PPSCh. 9.3 - Prob. 9PPSCh. 9.3 - Prob. 10PPSCh. 9.3 - Prob. 11PPSCh. 9.3 - Prob. 12PPSCh. 9.3 - Prob. 13PPSCh. 9.3 - Prob. 14PPSCh. 9.3 - Prob. 15PPSCh. 9.3 - Prob. 16PPSCh. 9.3 - Prob. 17PPSCh. 9.3 - Prob. 18PPSCh. 9.3 - Prob. 19PPSCh. 9.3 - Prob. 20PPSCh. 9.3 - Prob. 21PPSCh. 9.3 - Prob. 22PPSCh. 9.3 - Prob. 23PPSCh. 9.3 - Prob. 24PPSCh. 9.3 - Prob. 25PPSCh. 9.3 - Prob. 26PPSCh. 9.3 - Prob. 27PPSCh. 9.3 - Prob. 28PPSCh. 9.3 - Prob. 29PPSCh. 9.3 - Prob. 30PPSCh. 9.3 - Prob. 31PPSCh. 9.3 - Prob. 32PPSCh. 9.3 - Prob. 33PPSCh. 9.3 - Prob. 34PPSCh. 9.3 - Prob. 35HPCh. 9.3 - Prob. 36HPCh. 9.3 - Prob. 37HPCh. 9.3 - Prob. 38HPCh. 9.3 - Prob. 39HPCh. 9.3 - Prob. 40STPCh. 9.3 - Prob. 41STPCh. 9.3 - Prob. 42STPCh. 9.3 - Prob. 43STPCh. 9.3 - Prob. 44SRCh. 9.3 - Prob. 45SRCh. 9.3 - Prob. 46SRCh. 9.3 - Prob. 47SRCh. 9.3 - Prob. 48SRCh. 9.3 - Prob. 49SRCh. 9.3 - Prob. 50SRCh. 9.3 - Prob. 51SRCh. 9.3 - Prob. 52SRCh. 9.3 - Prob. 53SRCh. 9.3 - Prob. 54SRCh. 9.3 - Prob. 55SRCh. 9.3 - Prob. 56SRCh. 9.3 - Prob. 57SCh. 9.3 - Prob. 58SCh. 9.3 - Prob. 59SCh. 9.3 - Prob. 60SCh. 9.3 - Prob. 61SCh. 9.3 - Prob. 62SCh. 9.4 - Prob. 1CYUCh. 9.4 - Prob. 2CYUCh. 9.4 - Prob. 3CYUCh. 9.4 - Prob. 4CYUCh. 9.4 - Prob. 5CYUCh. 9.4 - Prob. 6CYUCh. 9.4 - Prob. 7CYUCh. 9.4 - Prob. 8CYUCh. 9.4 - Prob. 9CYUCh. 9.4 - Prob. 10PPSCh. 9.4 - Prob. 11PPSCh. 9.4 - Prob. 12PPSCh. 9.4 - Prob. 13PPSCh. 9.4 - Prob. 14PPSCh. 9.4 - Prob. 15PPSCh. 9.4 - Prob. 16PPSCh. 9.4 - Prob. 17PPSCh. 9.4 - Prob. 18PPSCh. 9.4 - Prob. 19PPSCh. 9.4 - Prob. 20PPSCh. 9.4 - Prob. 21PPSCh. 9.4 - Prob. 22PPSCh. 9.4 - Prob. 24PPSCh. 9.4 - Prob. 25PPSCh. 9.4 - Prob. 26PPSCh. 9.4 - Prob. 27PPSCh. 9.4 - Prob. 28PPSCh. 9.4 - Prob. 29PPSCh. 9.4 - Prob. 30PPSCh. 9.4 - Prob. 31PPSCh. 9.4 - Prob. 32PPSCh. 9.4 - Prob. 33PPSCh. 9.4 - Prob. 34PPSCh. 9.4 - Prob. 35PPSCh. 9.4 - Prob. 36PPSCh. 9.4 - Prob. 37PPSCh. 9.4 - Prob. 38PPSCh. 9.4 - Prob. 39PPSCh. 9.4 - Prob. 40PPSCh. 9.4 - Prob. 41PPSCh. 9.4 - Prob. 42PPSCh. 9.4 - 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Prob. 76SCh. 9.5 - Prob. 77SCh. 9.5 - Prob. 1CYPCh. 9.5 - Prob. 2ACYPCh. 9.5 - Prob. 2BCYPCh. 9.5 - Prob. 3ACYPCh. 9.5 - Prob. 3BCYPCh. 9.5 - Prob. 4ACYPCh. 9.5 - Prob. 4BCYPCh. 9.5 - Prob. 1CYUCh. 9.5 - Prob. 2CYUCh. 9.5 - Prob. 3CYUCh. 9.5 - Prob. 4CYUCh. 9.5 - Prob. 5CYUCh. 9.5 - Prob. 6CYUCh. 9.5 - Prob. 7CYUCh. 9.5 - Prob. 8CYUCh. 9.5 - Prob. 9CYUCh. 9.5 - Prob. 10CYUCh. 9.5 - Prob. 11CYUCh. 9.5 - Prob. 12CYUCh. 9.5 - Prob. 13CYUCh. 9.5 - Prob. 14CYUCh. 9.5 - Prob. 15CYUCh. 9.5 - Prob. 16PPSCh. 9.5 - Prob. 17PPSCh. 9.5 - Prob. 18PPSCh. 9.5 - Prob. 19PPSCh. 9.5 - Prob. 20PPSCh. 9.5 - Prob. 21PPSCh. 9.5 - Prob. 22PPSCh. 9.5 - Prob. 23PPSCh. 9.5 - Prob. 24PPSCh. 9.5 - Prob. 25PPSCh. 9.5 - Prob. 26PPSCh. 9.5 - Prob. 27PPSCh. 9.5 - Prob. 29PPSCh. 9.5 - Prob. 30PPSCh. 9.5 - Prob. 31PPSCh. 9.5 - Prob. 32PPSCh. 9.5 - Prob. 33PPSCh. 9.5 - Prob. 34PPSCh. 9.5 - Prob. 35PPSCh. 9.5 - Prob. 36PPSCh. 9.5 - Prob. 37PPSCh. 9.5 - Prob. 38PPSCh. 9.5 - Prob. 39PPSCh. 9.5 - Prob. 40PPSCh. 9.5 - Prob. 43PPSCh. 9.5 - 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Prob. 34PPSCh. 9.8 - Prob. 35PPSCh. 9.8 - Prob. 36PPSCh. 9.8 - Prob. 37PPSCh. 9.8 - Prob. 38HPCh. 9.8 - Prob. 39HPCh. 9.8 - Prob. 40HPCh. 9.8 - Prob. 41HPCh. 9.8 - Prob. 42HPCh. 9.8 - Prob. 43STPCh. 9.8 - Prob. 44STPCh. 9.8 - Prob. 45STPCh. 9.8 - Prob. 46STPCh. 9.8 - Prob. 47SRCh. 9.8 - Prob. 48SRCh. 9.8 - Prob. 49SRCh. 9.8 - Prob. 50SRCh. 9.8 - Prob. 51SRCh. 9.8 - Prob. 52SRCh. 9.8 - Prob. 53SRCh. 9.8 - Prob. 54SRCh. 9.8 - Prob. 55SRCh. 9.8 - Prob. 56SRCh. 9.8 - Prob. 57SRCh. 9.8 - Prob. 58SRCh. 9.8 - Prob. 59SRCh. 9.8 - Prob. 60SRCh. 9.8 - Prob. 61SRCh. 9.8 - Prob. 62SRCh. 9.8 - Prob. 63SRCh. 9.8 - Prob. 64SCh. 9.8 - Prob. 65SCh. 9.8 - Prob. 66SCh. 9.8 - Prob. 67SCh. 9.8 - Prob. 68SCh. 9.8 - Prob. 69SCh. 9.8 - Prob. 1ACYPCh. 9.8 - Prob. 1BCYPCh. 9.8 - Prob. 1CCYPCh. 9.8 - Prob. 2ACYPCh. 9.8 - Prob. 2BCYPCh. 9.8 - Prob. 3CYPCh. 9.8 - Prob. 4CYPCh. 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. 31PPSCh. 9.8 - Prob. 32PPSCh. 9.9 - Prob. 1ACYPCh. 9.9 - Prob. 1BCYPCh. 9.9 - Prob. 2ACYPCh. 9.9 - Prob. 2BCYPCh. 9.9 - Prob. 3ACYPCh. 9.9 - Prob. 3BCYPCh. 9.9 - Prob. 4CYPCh. 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. 12CYUCh. 9.9 - Prob. 13CYUCh. 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. 31HPCh. 9.9 - Prob. 32HPCh. 9.9 - Prob. 33HPCh. 9.9 - Prob. 34HPCh. 9.9 - Prob. 36STPCh. 9.9 - Prob. 37STPCh. 9.9 - Prob. 38STPCh. 9.9 - Prob. 39STPCh. 9.9 - Prob. 40SRCh. 9.9 - Prob. 41SRCh. 9.9 - Prob. 42SRCh. 9.9 - Prob. 43SRCh. 9.9 - Prob. 44SRCh. 9.9 - Prob. 45SRCh. 9.9 - Prob. 46SRCh. 9.9 - Prob. 47SRCh. 9.9 - Prob. 48SRCh. 9.9 - Prob. 49SRCh. 9.9 - Prob. 50SRCh. 9.9 - Prob. 51SRCh. 9.9 - Prob. 52SRCh. 9.9 - Prob. 53SRCh. 9.9 - Prob. 54SRCh. 9.9 - Prob. 55SRCh. 9.9 - Prob. 56SRCh. 9.9 - Prob. 57SRCh. 9.9 - Prob. 58SRCh. 9.9 - Prob. 59SRCh. 9.9 - Prob. 60SCh. 9.9 - Prob. 61SCh. 9.9 - Prob. 62SCh. 9.9 - Prob. 35HPCh. 9 - Prob. 5STPCh. 9 - Prob. 6STPCh. 9 - Prob. 7STPCh. 9 - Prob. 8STPCh. 9 - Prob. 9STPCh. 9 - Prob. 10STPCh. 9 - Prob. 11STPCh. 9 - Prob. 1QCCh. 9 - Prob. 2QCCh. 9 - Prob. 3QCCh. 9 - Prob. 4QCCh. 9 - Prob. 5QCCh. 9 - Prob. 6QCCh. 9 - Prob. 7QCCh. 9 - Prob. 8QCCh. 9 - Prob. 9QCCh. 9 - Prob. 10QCCh. 9 - Prob. 11QCCh. 9 - Prob. 12QCCh. 9 - Prob. 13QCCh. 9 - Prob. 14QCCh. 9 - Prob. 15QCCh. 9 - Prob. 16QCCh. 9 - Prob. 17QCCh. 9 - Prob. 18QCCh. 9 - Prob. 19QCCh. 9 - Prob. 20QCCh. 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. 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. 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. 1STPCh. 9 - Prob. 2STPCh. 9 - Prob. 3STPCh. 9 - Prob. 4STP

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