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 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 A Bridge To Success Algebra 2: Student Edition 2015

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