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

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Question
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Chapter 5.7, Problem 1E
To determine

To graph: the quadratic equation as mentioned in the problem.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The quadratic equation is y=−x2+2x−1.

Graph:

The graph mentioned below is in real number line of x axis and y axis.

Where vertex (1,0).

Algebra 2, Chapter 5.7, Problem 1E , additional homework tip 1

Interpretation:

Consider the quadratic equation y=−x2+2x−1.

The mentioned quadratic equation above will be in vertex form y=a(x−h)2+k where (h,k) is the vertex.

We can write the mentioned quadratic equation in the vertex form as y=−x2+2x−1⇒y=−(x2−2x+1)⇒y=−(x−1)2.

Therefore the vertex form of the equation is y=−(x−1)2+0.

Which is comparable to y=a(x−h)2+k where a=−1 which is less than 0.

Since a<0 the direction of graph will be negative side of y axis and the vertex is (1,0).

The discriminant of standard form of quadratic equation y=−x2+2x−1 is D=b2−4*a*c⇒D=(2)2−4*(−1)*(−1)=4−4=0.

Here D=0.

Therefore the graph will lie on x axis.

At x=0 the y=−x2+2x−1 will yield y=−1.

Therefore graph will cut y axis at (0,−1).

Therefore the graph will be as mentioned below.

  Algebra 2, Chapter 5.7, Problem 1E , additional homework tip 2

To determine

To draw: the table for the equation y=−x2+2x−1.

Expert Solution
Check Mark

Answer to Problem 1E

The table of the equation is

  xy−3−16−2−9−1−40−1102−13−4.

Explanation of Solution

Given information:

The equation is y=−x2+2x−1 and the value of x is −3,−2,−1,0,1,2,3.

Formula:

We will substitute the value of x in the equation y=−x2+2x−1.

Calculation:

Consider the equation y=−x2+2x−1.

Since the value of x is −3,−2,−1,0,1,2,3.

Recall that we will substitute the value of x in the equation y=−x2+2x−1.

Therefore

At x=−3⇒y=−(−3*−3)+2(−3)−1=−16.

At x=−2⇒y=−(−2*−2)+2(−2)−1=−9..

At x=−1⇒y=−(−1*−1)+2(−1)−1=−4..

At x=0⇒y=−(0*0)+2(0)−1=−1..

At x=1⇒y=−(1*1)+2(1)−1=0.

At x=2⇒y=−(2*2)+2(2)−1=−1.

At x=3⇒y=−(3*3)+2(3)−1=−4.

Therefore the table will be as mentioned below.

  xy−3−16−2−9−1−40−1102−13−4

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Chapter 5.7, Problem 76S
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Chapter 5.7, Problem 2E

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
Ch. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYUCh. 5.1 - Prob. 5CYUCh. 5.1 - Prob. 6CYUCh. 5.1 - Prob. 7CYUCh. 5.1 - Prob. 8CYUCh. 5.1 - Prob. 9CYUCh. 5.1 - Prob. 10CYUCh. 5.1 - Prob. 11CYUCh. 5.1 - Prob. 12PPSCh. 5.1 - Prob. 13PPSCh. 5.1 - Prob. 14PPSCh. 5.1 - Prob. 15PPSCh. 5.1 - Prob. 16PPSCh. 5.1 - Prob. 17PPSCh. 5.1 - Prob. 18PPSCh. 5.1 - Prob. 19PPSCh. 5.1 - Prob. 20PPSCh. 5.1 - Prob. 21PPSCh. 5.1 - Prob. 22PPSCh. 5.1 - Prob. 23PPSCh. 5.1 - Prob. 24PPSCh. 5.1 - Prob. 25PPSCh. 5.1 - Prob. 26PPSCh. 5.1 - Prob. 27PPSCh. 5.1 - Prob. 28PPSCh. 5.1 - Prob. 29PPSCh. 5.1 - Prob. 30PPSCh. 5.1 - Prob. 31PPSCh. 5.1 - Prob. 32PPSCh. 5.1 - Prob. 33PPSCh. 5.1 - Prob. 34PPSCh. 5.1 - Prob. 35PPSCh. 5.1 - Prob. 36PPSCh. 5.1 - Prob. 37PPSCh. 5.1 - Prob. 38PPSCh. 5.1 - Prob. 39PPSCh. 5.1 - Prob. 40PPSCh. 5.1 - Prob. 41PPSCh. 5.1 - Prob. 42PPSCh. 5.1 - Prob. 43PPSCh. 5.1 - Prob. 44PPSCh. 5.1 - Prob. 45PPSCh. 5.1 - Prob. 46PPSCh. 5.1 - Prob. 47PPSCh. 5.1 - Prob. 48PPSCh. 5.1 - Prob. 49PPSCh. 5.1 - 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Prob. 1BCYPCh. 5.4 - Prob. 2ACYPCh. 5.4 - Prob. 2BCYPCh. 5.4 - Prob. 2CCYPCh. 5.4 - Prob. 3ACYPCh. 5.4 - Prob. 3BCYPCh. 5.4 - Prob. 4CYPCh. 5.4 - Prob. 5ACYPCh. 5.4 - Prob. 5BCYPCh. 5.4 - Prob. 6CYPCh. 5.4 - Prob. 7ACYPCh. 5.4 - Prob. 7BCYPCh. 5.4 - Prob. 1CYUCh. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 3CYUCh. 5.4 - Prob. 4CYUCh. 5.4 - Prob. 5CYUCh. 5.4 - Prob. 6CYUCh. 5.4 - Prob. 7CYUCh. 5.4 - Prob. 8CYUCh. 5.4 - Prob. 9CYUCh. 5.4 - Prob. 10CYUCh. 5.4 - Prob. 11CYUCh. 5.4 - Prob. 12CYUCh. 5.4 - Prob. 13CYUCh. 5.4 - Prob. 14CYUCh. 5.4 - Prob. 15CYUCh. 5.4 - Prob. 16CYUCh. 5.4 - Prob. 17CYUCh. 5.4 - Prob. 18PPSCh. 5.4 - Prob. 19PPSCh. 5.4 - Prob. 20PPSCh. 5.4 - Prob. 21PPSCh. 5.4 - Prob. 22PPSCh. 5.4 - Prob. 23PPSCh. 5.4 - Prob. 24PPSCh. 5.4 - Prob. 25PPSCh. 5.4 - Prob. 26PPSCh. 5.4 - Prob. 27PPSCh. 5.4 - Prob. 28PPSCh. 5.4 - Prob. 29PPSCh. 5.4 - Prob. 30PPSCh. 5.4 - Prob. 31PPSCh. 5.4 - Prob. 32PPSCh. 5.4 - Prob. 33PPSCh. 5.4 - Prob. 34PPSCh. 5.4 - Prob. 35PPSCh. 5.4 - Prob. 36PPSCh. 5.4 - Prob. 37PPSCh. 5.4 - 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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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