BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.9, Problem 9E
To determine

To graph: The quadratic equation y=10+25xx3 in a graphing window.

Expert Solution

Explanation of Solution

Given information:

The quadratic equation y=10+25xx3 .

Graph:

The graph of the quadratic equation y=10+25xx3 can be sketched in the cartesian plane,

Consider the quadratic equation, y=10+25xx3 .

Rewrite the given equation:

  y=10+25xx3y=x3+25x+10y=x(25x2)+10 ,

Now put the values of x in the equation to find the values of y or to find the real roots of y with the help of x .

Substitute the value of x=3 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=3(25(3)2)+10y=3(259)+10y=3×16+10

The value of y is:

  y=3×16+10y=48+10y=38

Substitute the value of x=2 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=2(25(2)2)+10y=2(254)+10y=2×21+10

The value of y is:

  y=2×21+10y=42+10y=32

Substitute the value of x=1 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=1(25(1)2)+10y=1(251)+10y=1×24+10

The value of y is:

  y=1×24+10y=24+10y=14

Substitute the value of x=0 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=0(25(0)2)+10y=0(25)+10y=10

Substitute the value of x=1 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=1(25(1)2)+10y=1(251)+10y=1×24+10

The value of y is:

  y=24+10y=34

Substitute the value of x=2 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=2(25(2)2)+10y=2(254)+10y=2×21+10

The value of y is:

  y=2×21+10y=42+10y=52

Substitute the value of x=3 in equation y=x(25x2)+10 :

  y=x(25x2)+10y=3(25(3)2)+10y=3(253)+10y=3×24+10

The value of y is:

  y=3×24+10y=72+10y=82

When the value of x is 3 then value of y is 38 .

Same as the value of x is 2 then value of y is 32 .

The value of x is 1 then value of y is 14 .

The value of x is 0 then value of y is 10 .

The value of x is 1 then value of y is 34 .

The value of x is 2 then value of y is 52 .

The value of x is 3 then value of y is 82 .

Observe that as the value of x increases there is the huge increment in value of y .

Same as the value of x decreases there is a decrement in the value of y .

Steps to plot the graph of the equation y=x3+25x+10 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function y=x3+25x+10 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=20Xmax=20Ymin=800Ymax=1000

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 9E , additional homework tip  1

Interpretation:

The equation of the function y=x3+25x+10 represents a parabola.

The equation has a wave formed graph.

The x intercepts are the points on xaxis where the graph of the equation touches xaxis .

Recall that the graphical approach to solve the equation simultaneously is observe the point where the graph of equation y=x3+25x+10 intersects the y -axis.

Therefore, the equation y=x3+25x+10 is symmetric about the y axis Initially the graph of the equation y=x3+25x+10 increases when increase the value of x .

a.When the x -axis ranges from [4,4] and y -axis ranges from [4,4] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x3+25x+10 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function y=x3+25x+10 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=4Xmax=4Ymin=4Ymax=4

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 9E , additional homework tip  2

This window is not perfect viewing window.

b.

When the x -axis ranges from [10,10] and y -axis ranges from [10,10] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x3+25x+10 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function y=x3+25x+10 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=10Xmax=10Ymin=10Ymax=10

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 9E , additional homework tip  3

This window is not a perfect viewing window.

c.

When the x -axis ranges from [20,20] and y -axis ranges from [100,100] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x3+25x+10 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function y=x3+25x+10 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=20Xmax=20Ymin=100Ymax=100

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 9E , additional homework tip  4

This is the perfect viewing window.

d.

When the x -axis ranges from [100,100] and y -axis ranges from [200,200] their graph obtained in the screen is provided below.

Steps to plot the graph of the equation y=x3+25x+10 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function y=x3+25x+10 .

Step 6: Press WINDOW key. Change the settings to

  Xmin=100Xmax=100Ymin=200Ymax=200

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 9E , additional homework tip  5

This window has large view, in this the graph points are not clear.

So the perfect viewing window of the graph y=x3+25x+10 is option ‘ c[20,20]by[100,100] .

The perfect viewing window is [20,20]by[100,100] , option ‘ c ’.

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