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Chapter 6: Q41. (page 291)

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

f(x)=-20x+5x2+9

Short Answer

Expert verified

The function has minimum value that is -11.

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)=-20x+5x2+9=5x2-20x+9

03

Step 3. Solution.

In the function f(x)=5x2-20x+9, we have a=5,b=-20,c=9

Here, a=5>0

So, the graph opens up and has a minimum value.

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

Thex-coordinate of the vertex is

鈭�b2a=鈭�鈭�202(5)..........a=5,b=鈭�20=2

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

f(2)=522-202+9=-11

So, the minimum value of function is -11.

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Most popular questions from this chapter

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

x2-2x-1=0

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=0.5x2-1

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

f(x)=x2-8x+2

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

fx=3x2-7x+2

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

-x2+x=-20
See all solutions

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