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Chapter 6: Q42. (page 291)

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=-12x2-2x+3

Short Answer

Expert verified

The function has maximum value that is 5.

Step by step solution

01

Step 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a鈮�0, the x-coordinate of vertex is -b2a.

The graph of f(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
02

Step 2. Given Information.

The given function is f(x)=-12x2-2x+3

03

Step 3. Solution.

In the function f(x)=-12x2-2x+3, we have a=-12,b=-2,c=3

Here, a=-12<0

So, the graph opens down and has a maximum value.

The maximum value of the function is the y-coordinate of the vertex.

Thex-coordinate of the vertex is

鈭�b2a=鈭�鈭�22(鈭�12)..........a=鈭�12,b=鈭�2=鈭�2

Find they-coordinate of the vertex by evaluating the function for x=-2.

f(-2)=-12-22-2-2+3=5

So, the maximum value of function is 5.

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Most popular questions from this chapter

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WRITING IN MATH Answer the question that was posed at the beginning of the lesson.

How can income from a rock concert be maximized?

Include the following in your answer:

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increases, and

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