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 60E

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 60E

The minimum value of the function is −814 , the function is decreasing from (−∞,−32) and is increasing from (−32,∞) .

Explanation of Solution

Given information:

The function: h(x)=x2+3x−18

Calculation:

The given function is h(x)=x2+3x−18 .

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

h(x)+(32)2=(x2+3x+(32)2)−18h(x)+94=(x2+3x+94)−18h(x)=(x+32)2−18−94h(x)=(x+32)2−814

In the above equation it is seen that the vertex is (h,k)=(−32,−814) .

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

Since, in the above equation the value of a is positive; so the parabola opens up.

Thus, the parabola has a minimum value of −814 .

The parabola opens up. This means the graph is decreasing from (−∞,−32) and is increasing from (−32,∞) .

Hence, the minimum value of the function is −814 , the function is decreasing from (−∞,−32) and is increasing from (−32,∞) .

Chapter 3.6, Problem 59E

Chapter 3, Problem 1CR

Chapter 3 Solutions

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

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