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Chapter 3: Q. 7 (page 175)

Determine whether f(x)=-2x2+12x+3has a maximum or minimum value. Then find the maximum or minimum value.

Short Answer

Expert verified

The quadratic function has a maximum value. The maximum value is21.

Step by step solution

01

Step 1. Given information. 

Determine whether f(x)=-2x2+12x+3 has a maximum or minimum value. Then find the maximum or minimum value.

02

Step 2. Compare the function.

Compare

f(x)=-2x2+12x+3tof(x)=ax2+bx+cThena=-2,b=12andc=3

Since a<0the graph of f opens down, so the vertex is a maximum value occurs at

x=-b2a=-122-2=124=3

The maximum value is

f-b2a=f(3)=-232+123+3=-18+36+3=21

03

Step 3. Conclusion.  

The quadratic function has a maximum value. The maximum value is21.

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Most popular questions from this chapter

Match each graph to one the following functions.

f(x)=x2+2x+1

State the circumstances that cause the graph of a quadratic function f(x)=ax2+bx+cto have no x-intercepts.

Match each graph to one the following functions.

f(x)=x2-2x+2

A is used to help us to see the type of relation, if any, that may exist between two variables.

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
See all solutions

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