PRECALCULUS:GRAPHICAL,...-NASTA ED.

10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Expert Solution & Answer

Chapter P.4, Problem 67E

Solution

a.

The graph for a=3, b=−2 .

Given:

The equation, xa+yb=c, a≠0, b≠0, c=1

Concept Used:

The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.

Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1

The slope of a line is defined as rise over run

Calculation:

For the values a=3, b=−2 , the given equation becomes

x3+y−2=1x3−y2=1

The graph of the equation is shown below:

b.

The graph for a=−2, b=−3 .

Given:

The equation, xa+yb=c, a≠0, b≠0, c=1

Concept Used:

The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.

Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1

The slope of a line is defined as rise over run

Calculation:

For the values a=−2, b=−3 , the given equation becomes

x−2+y−3=1−x2−y3=1

The graph of the equation is shown below:

c.

The graph for a=5, b=3 .

Given:

The equation, xa+yb=c, a≠0, b≠0, c=1

Concept Used:

The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.

Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1

The slope of a line is defined as rise over run

Calculation:

For the values a=5, b=3 , the given equation becomes

x5+y3=1

The graph of the equation is shown below:

d.

The conjecture for the graphs from (a) through (c).

The value of a represents the x -intercept of the graph and the value of b represents the y -intercept of the graph when value of c is 1.

Given:

The equation, xa+yb=c, a≠0, b≠0, c=1

Concept Used:

The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.

Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1

The slope of a line is defined as rise over run

Calculation:

From the above graphs observe that the value of a represents the x -intercept of the graphs and the value of b represents the y -intercept of the graphs when value of c is 1.

Chapter P.4, Problem 66E

Chapter P.4, Problem 68E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY

Solution Summary: The graph of the equation for a=2,b=-2 is shown below.

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Chapter P Solutions