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Chapter 3: Q. 16 (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)=-x2+8x-4

Short Answer

Expert verified

The quadratic function has a maximum value. The maximum value is 12.

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)=-x2+8x-4

02

Step 2. Compare the function.

Compare

f(x)=-x2+8x-4tof(x)=ax2+bx+cThena=-1,b=8andc=-4

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

x=-b2a=-82(-1)=4

The maximum value is

f(-b2a)=f(4)=-42+84-4=-16+32-4=12

03

Step 3. Conclusion. 

The quadratic function has a maximum value. The maximum value is 12.

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Most popular questions from this chapter

To graph y=(x-4)2, you shift the graph of y=x2to the ______ a distance of ______ units.

Solve:60x-900=-15x+2850.

Match each graph to one the following functions.

f(x)=-x2-1

If f(x)=14x-3,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant

In Problems 6鈥� 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).

fx=x-22+2
See all solutions

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