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Chapter 3: Q. 14 (page 155)

Match each graph to one the following functions.

f(x)=x2+2x+1

Short Answer

Expert verified

The required graph is in option A.

Step by step solution

01

Step 1. Given information.

The given function is:

f(x)=x2+2x+1

It can be written as:

f(x)=(x+1)2 [鈭�(a+b)2=a2+2ab+b2]

02

Step 2. Identify the graph of the function.

The vertex of the function f(x)=a(x-h)2+kis (h,k). The graph opens up if a>0and it opens down if a<0.

In the given function a=1,h=-1,k=0. So, the graph must be an upward parabola with vertex at (-1,0).


03

Step 3. Conclusion.

The required graph is in option A.

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Most popular questions from this chapter

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)=23x2+43x-1

If G(x)=-2,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.

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

The monthly revenue R achieved by selling

x wristwatches is figured to be R(x)=75x-0.2x2The monthly cost C of selling x wristwatches isC(x)=32x+1750

(a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue?

(b) Profit is given as P(x) = R(x) - C(x). What is the profit function?

(c) How many wristwatches must the firm sell to maximize

profit? What is the maximum profit?

(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.

In problems 3-6, use the figure to solve each inequality.

a) f(x)>0

b)f(x)鈮�0
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