To graph : The equations y = − 3 x 2 + 6 x − 1 2 , y = 7 − 7 12 x 2 in the viewing rectangle [ − 4 , 4 ] by [ − 1 , 3 ] and identify the intersection points.

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1.9, Problem 23E
To determine

To graph: The equations y=−3x2+6x−12,y=7−712x2 in the viewing rectangle [−4,4]by[−1,3] and identify the intersection points.

Expert Solution

Explanation of Solution

Given information:

The equations y=3x2+6x12,y=7712x2 and viewing rectangle [4,4]by[1,3] .

Graph:

The graph of the equation y=3x2+6x12 can be sketched using the table,

 x y 0 −12 2 −12 4 −492 −2 −492 −4 −732

The graph of equation is provided below,

The graph of the equation y=7712x2 can be sketched using the table,

 x y 0 7 2 143 4 73 −2 143 −4 73

The graph of equation is provided below,

The graph of both equations in same figure is provided below,

From the graph it looks as the graphs intersect near the (1,3) .Zoom the area near this point.

Since, the graphs never intersecteach other so there is no intersecting points.

Interpretation:

The graph of an equation in a viewing screen is a viewing rectangle.

The x -values to range from a minimum value of xmin =a to a maximum value of xmax =b

The y -values to range from minimum value of ymin =c to a maximum value of ymax =d

Then, the display portion of the graph lies in the rectangle [a,b]×[c,d]={(x,y)|axb,cyd}

The equations y=3x2+6x12,y=7712x2 are not intersect in viewing rectangle [4,4]by[1,3] .They almost touch but never intersect each other at any point.

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