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 18E
To determine

To graph: The quadratic equation y=x((x+6)(x9)) in a graphing window.

Expert Solution

Explanation of Solution

Given information:

The quadratic equation y=x((x+6)(x9)) .

Graph:

The graph of the quadratic equation y=x((x+6)(x9)) can be sketched in the cartesian plane,

Consider the quadratic equation, y=x((x+6)(x9)) .

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 .

Rewrite the equation as y=0 :

  x((x+6)(x9))=yx((x+6)(x9))=0

Either x=0 or x+6=0 , x9=0 .

Hence x=0 and x=6 , x=9

Now substitute the value of x=0 in equation y=x((x+6)(x9)) .

  y=x((x+6)(x9))y=0((0+6)(09))y=0

Now put the value of x=1 in the equation, y=x((x+6)(x9)) .

  y=x((x+6)(x9))y=1((1+6)(19))y=1((7)(8))y=56

Substitute the value x=2 in the equation y=x((x+6)(x9)) :

  y=x((x+6)(x9))y=2((2+6)(29))y=2((8)(7))y=256

Now the value of y is:

  y=2((8)(7))y=256y=112

Substitute the value x=3 in the equation y=x((x+6)(x9)) :

  y=x((x+6)(x9))y=3((3+6)(39))y=3((9)(6))y=354

Now the value of y is:

  y=3((9)(6))y=354y=162

Substitute the value x=1 in the equation y=x((x+6)(x9)) :

  y=x((x+6)(x9))y=1((1+6)(19))y=1((5)(10))y=50

Substitute the value x=2 in the equation y=x((x+6)(x9)) :

  y=x((x+6)(x9))y=2((2+6)(29))y=2((4)(11))y=244

Now the value of y is:

  y=2((4)(11))y=244y=88

Substitute the value x=3 in the equation y=x((x+6)(x9)) :

  y=x((x+6)(x9))y=3((3+6)(39))y=3((3)(12))y=336

Now the value of y is:

  y=3((3)(12))y=336y=108

Observed that when the value of x increases then the value of y decreases slightly.

When the value of x decreases then the value of y increases slightly.

Steps to plot the graph of the equation y=x((x+6)(x9)) 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 x((x+6)(x9)) .

Step 6: Press WINDOW key. Change the settings to

  Xmin=50Xmax=50Ymin=250Ymax=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 18E

Interpretation:

The equation of the function y=x((x+6)(x9)) represents a wave graph.

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

At x -axis y is always zero.

Recall that the graphical approach to solve the equation simultaneously.

Therefore, the equation y=x((x+6)(x9)) is symmetric about the y axis Initially the graph of the function y=x((x+6)(x9)) increases when increase the value of x ,the graph is a parabola shaped graph.

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