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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Question

Chapter 3.6, Problem 59E

To determine

To calculate: The minimum value and maximum value of the function. Also, describe where the function is increasing and decreasing.

Expert Solution & Answer

Answer to Problem 59E

The maximum value of the function is 25, the function is increasing from (−∞,−2) and is decreasing from (−2,∞) .

Explanation of Solution

Given information:

The function: f(x)=−(x−3)(x+7)

Calculation:

The given function is f(x)=−(x−3)(x+7) .

Rewrite the function as:

f(x)=−(x−3)(x+7)f(x)=−(x2+7x−3x−21)f(x)=−(x2+4x−21)f(x)=−x2−4x+21

Write the function in the vertex form a(x−h)2+k as:

f(x)+(−1)(4)=−(x2+4x+4)+21f(x)−4=−(x+2)2+21f(x)=−(x+2)2+21+4f(x)=−(x+2)2+25

In the above equation it is seen that the vertex is (h,k)=(−2,25) .

The value of k is the maximum/minimum value of a function.

Since, in the above equation the value of a is negative; so the parabola opens down.

Thus, the parabola has a maximum value of 25.

The parabola opens down. This means the graph is increasing from (−∞,−2) and is decreasing from (−2,∞) .

Hence, the maximum value of the function is 25, the function is increasing from (−∞,−2) and is decreasing from (−2,∞) .

Chapter 3.6, Problem 58E

Chapter 3.6, Problem 60E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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