BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Concept explainers

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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Question

Chapter 2.2, Problem 75E

To determine

To draw: The curve of the arch and find the domain and the range of the function, and their representation.

Expert Solution & Answer

Answer to Problem 75E

The domain of the graph represents the distance covered by the arch and the domain is (126,0) .

The range represents the distance covered vertically by the arch and the range is, (0,60) .

The equation of the graph is y=−0.01259(x−63)2+50 .

Explanation of Solution

Given Information: The arch is modeled by the parabola and can reach a maximum height of 50 meters at a point approximately 63 meters across the river.

Calculation:

The domain of the graph represents the distance covered by the arch. This can be calculated by calculating the x -coordinates of the graph. Here, the arch reaches maximum height at approximately 63 meters. The total distance covered by the arch can be calculated by multiplying 63 by 2,

x=63×2=126

Hence, the domain is (126,0) .

The range represents the distance covered vertically by the arch.

Since the maximum height that could be reached is 50, the range is, (0,60) .

To graph the arch, which is in the shape of parabola, first write the equation.

Equation of the parabola in standard form is,

y=a(x−h)2+k where (h,k) is the vertex.

Since the vertex of the parabola made by arch is (63,50) , the value of a at the starting point that (0,0) is,

0=a(0−63)2+500=3969a+50a=−503969=−0.01259

Hence the equation of the graph is,

y=−0.01259(x−63)2+50

The graph is,

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 2.2, Problem 75E

Chapter 2.2, Problem 74E

Chapter 2.2, Problem 76E

Chapter 2 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - 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