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Chapter 3: Q. 15 (page 174)

In Problems 15鈥�17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.

f(x)=3x2-6x+4

Short Answer

Expert verified

The quadratic function has a minimum value. The minimum value is1.

Step by step solution

01

Step 1. Given information.

Determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.

f(x)=3x2-6x+4

02

Step 2. Compare the function.

Compare f(x)=3x2-6x+4tof(x)=ax2+bx+cThena=3,b=-6andc=4

Since a>0, the graph of f opens up, so the vertex is a minimum value occurs at

x=-b2a=--62(3)=66=1

The minimum value is

f-b2a=f(1)=3(1)2-6(1)+4=3-6+4=1

03

Step 3. Conclusion.

The quadratic function has a minimum value. The minimum value is1.

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Most popular questions from this chapter

True or False The average rate of change of f(x)=2x+8is8.

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=2x2-4x+1

Graph the function fby starting with the graph of y=x2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

f(x)=(x+2)2-2

Match each graph to one the following functions.

f(x)=-x2-1

Match each graph to one the following functions.

f(x)=x2-2x+1
See all solutions

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