Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 9.1, Problem 19CYU
To determine

To Graph:

The given function.

Expert Solution & Answer
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Explanation of Solution

Given Information:

Given equation is :

  y=2x28x4

Concept Used :

  • Quadratic Functions:
  • Quadratic functions are non-linear and are of the form:

  f(x)=ax2+bx+c;a0

This is the standard form of Quadratic function.

  • Shape of the graph of a Quadratic function is called Parabola.
  • Parabolas are symmetric about a central line called Axis Of Symmetry.
  • The axis of symmetry intersects a parabola only at one point , called the Vertex.
  • Parent Function:

  y=x2

  • Standard Form :

  f(x)=ax2+bx+c;a0

  • Type of Graph:

Parabola

  • Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.

  x=b2a

  • y-intercept = The y coordinate of the point at which the graph intersects y-axis = c
  • Graph:

  Algebra 1, Chapter 9.1, Problem 19CYU , additional homework tip  1

  • If a > 0 ,
  • The graph of ax2+bx+c opens upward.
  • The lowest point on the graph is the minimum.
  • If a < 0 ,
  • The graph of ax2+bx+c opens downward.
  • The highest point on the graph is the maximum.
  • The maximum or the minimum is the vertex.

Calculation:

  • In the equation y=2x28x4 ; comparing it with standard form of quadratic equation , we have a = 2, b = -8 , c = -4 .
  • Find equation of Axis of Symmetry :

  y=ax2+bx+c...........................[standard_form]x=b2a.....................................[formula_of_axis_of_symmetry]x=82(2)=2..........................[a=2,b=8]

The equation of axis of symmetry is x=2

  • Find the Vertex and determine whether it is maximum or minimum:

Since axis of symmetry passes through the vertex , we have x coordinate of the vertex (x,y) is x=2

Substituting the value of x=2in the equation y=2x28x4

  y=2x28x4 y=2 (2) 2 8(2)4...............[x=2]y=8164..................................[simplify]y=12

The vertex is at (2,12) .

Since the a = 2 > 0 .So, the graph opens upward .Hence, the vertex is the minimum.

  • Find y-intercept :

The y-coordinate of the point at which the graph cuts the y-axis is the y-intercept.

y-intercept always occurs at (0,c) and c = -4 here.

So, y-intercept = -4 and point is (0,-4)

  • The axis of symmetry cuts the parabola into two equal parts . So, if there is a point on one side, there is a corresponding point on the other side that is at a same distance from the axis of symmetry and the same y-value.
    xy
    0-4
    1-10
    2-12
    3-10
    4-4
  • Connect the points with a smooth curve.

Graph :

  Algebra 1, Chapter 9.1, Problem 19CYU , additional homework tip  2

Chapter 9 Solutions

Algebra 1

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. 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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