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Chapter 3: Q. 13 (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 F.

Step by step solution

01

Step 1. Given information.

The given function is:

f(x)=x2-2x+1

It can be written as:

localid="1645873350675" f(x)=(x-1)2 [∵(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 F.

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Most popular questions from this chapter

On one set of coordinate axes, graph the family of parabolas f(x)=x2+bx+1for b = -4, b = 0, and b = 4. Describe the general characteristics of this family.

In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

If the slope m of the graph of a linear function is________, the function is increasing over its domain.

Find an equation of the line containing the points (1,4)and (3,8).

The daily revenue R achieved by selling x boxes of candy is figured to be R(x)=9.5x-0.04x2The daily cost C of selling x boxes of candy is C(x)=1.25x+250.

(a) How many boxes of candy 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 boxes of candy 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.
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