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Chapter 3: Q. 17 (page 155)

Match each graph to one the following functions.

f(x)=x2-2x

Short Answer

Expert verified

The required graph is in option H.

Step by step solution

01

Step 1. Write given function in vertex form.

The given function is:

f(x)=x2-2x

It can be written as:

f(x)=(x2-2x+1)-1f(x)=(x-1)2-1[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=-1. So, the graph must be an upward parabola with vertex at localid="1645876478996" (1,-1).

03

Step 3. Conclusion.

The required graph is in option H.

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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

In Problems 25鈥�32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

role="math" localid="1646199855131" (e)g(x)鈮�0(f)f(x)>g(x)(g)f(x)鈮�1

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.

In Problems 7鈥�22, solve each inequality.

4x2+9<6x

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)=3x2+6x
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