Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 2.2, Problem 49E

To determine

What is the height of the diving board.

Expert Solution

Answer to Problem 49E

The height of the diving board is 1 meter.

Explanation of Solution

Given information: The path of a diver is modeled by the function f(x)=−9x2+9x+1

Where f(x) is the height of the diver in meters above the water and x is the horizontal distance (in meters) from the end of the diving board.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 2.2, Problem 49E , additional homework tip 1

Calculation:

f(x)=−9x2+9x+1 ....................(1)

Height of the diving board can be calculated by putting x=0 into the function equation (1) because x=0 corresponds to distance 0 fron the end of the diving board. when x=0 diver still did not jump.

f(0)=−9×02+9×0+1=0+0+1=1 .

So ,the height of the diving board is 1 meter.

To determine

What is the maximum height of the diving board.

Expert Solution

Answer to Problem 49E

Maximum height of the diving board is 13/4 meter.

Explanation of Solution

Given information: The path of a diver is modeled by the function f(x)=−9x2+9x+1

Where f(x) is the height of the diver in meters above the water and x is the horizontal distance (in meters) from the end of the diving board.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 2.2, Problem 49E , additional homework tip 2

Calculation:

f(x)=−9x2+9x+1 ....................(1)

Identify the coefficients

a=−9 , b=9 , c=1.

Since a=−9<0 , parabola opens down and function has a maximum value.

To find maximum value, calculate coordinates of the vertex.

x=−b/2a=−9/2×(−9)=−9/−18=1/2. f(1/2)=(−9)× (1/2) 2 +9×(1/2)+1=(−9/4)+9/2+1=13/4

Maximum height of the diving board is 13/4 meter.

To determine

Describe where the diver is ascending and where the diver is descending.

Expert Solution

Answer to Problem 49E

Diver is ascending left to the x=1/2 and diver is descending right to the x=1/2 .

Explanation of Solution

Given information: The path of a diver is modeled by the function f(x)=−9x2+9x+1

Where f(x) is the height of the diver in meters above the water and x is the horizontal distance (in meters) from the end of the diving board.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 2.2, Problem 49E , additional homework tip 3

Calculation:

f(x)=−9x2+9x+1 ....................(1)

Identify the coefficients

a=−9 , b=9 , c=1.

Since a=−9<0 , parabola opens down and function has a maximum value.

To find maximum value, calculate coordinates of the vertex.

x=−b/2a=−9/2×(−9)=−9/−18=1/2. f(1/2)=(−9)× (1/2) 2 +9×(1/2)+1=(−9/4)+9/2+1=13/4

Since a=−9<0 , parabola opens down and vertex is at x=1/2 so, diver is ascending left to the x=1/2 and diver is descending right to the x=1/2 .

Chapter 2.2, Problem 48E

Chapter 2.2, Problem 50E

Chapter 2 Solutions

Big Ideas Math A Bridge To Success Algebra 2: 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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