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 17E
To determine

To graph: The quadratic equation y=0.01x3x2+5 in a graphing window.

Expert Solution

Explanation of Solution

Given information:

The quadratic equation y=0.01x3x2+5 .

Graph:

The graph of the quadratic equation y=0.01x3x2+5 can be sketched in the cartesian plane,

Consider the quadratic equation, y=0.01x3x2+5 .

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 take common:

  y=0.01x3x2+5y=0.01(x3100x2+500)

Now substitute the value of y in equation y=0.01(x3100x2+500) .

  y=0.01(x3100x2+500)0=0.01(x3100x2+500)0=(x3100x2+500)

Eliminate the quadratic term by substituting:

  y=x+1003x=y

  y=x+1003x=y1003

Now put the value of x in the equation, (x3100x2+500)=0 .

  (x3100x2+500)=0(y1003)3100(y1003)2+500=0

The value of x -intercepts are:

  x2.21174271x~2.2617928

Substitute the value x=0 in the equation y=0.01x3x2+5 :

  y=0.01x3x2+5y=0.01(0)302+5y=5

Substitute the value x=1 in the equation y=0.01x3x2+5 :

  y=0.01x3x2+5y=0.01(1)312+5y=0.011+5y=4.01

Substitute the value x=2 in the equation y=0.01x3x2+5 :

  y=0.01x3x2+5y=0.01(2)322+5y=0.0184+5y=1.08

Substitute the value x=1 in the equation y=0.01x3x2+5 :

  y=0.01x3x2+5y=0.01(1)3(1)2+5y=0.01+1+5y=5.99

Substitute the value x=2 in the equation y=0.01x3x2+5 :

  y=0.01x3x2+5y=0.01(2)3(2)2+5y=0.018+4+5y=9.08

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=0.01x3x2+5 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 0.01x3x2+5 .

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 17E

Interpretation:

The equation of the function y=0.01x3x2+5 represents a parabola.

The parabola opens downwards.

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, in the equation, y=0.01x3x2+5 there is no x intercepts.

Therefore, the equation y=0.01x3x2+5 is symmetric about the y axis Initially the graph of the function y=0.01x3x2+5 increases when increase the value of x ,the graph is a parabola shaped graph.

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