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Chapter 3: Q. 18 (page 155)

Match each graph to one the following functions.

f(x)=x2+2x+2

Short Answer

Expert verified

The required graph is in option D.

Step by step solution

01

Step 1. Write given function in vertex form.

The given function is:

f(x)=x2+2x+2

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 (-1,1).

03

Step 3. Conclusion.

The required graph is in option D.

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Most popular questions from this chapter

Match each graph to one the following functions.

f(x)=x2+2x+1

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

Match each graph to one the following functions.

f(x)=x2+2x

Suppose that f(x)=4x-1and g(x)=-2x+5

(a) Solve f(x)=0. (b) Solve f(x)>0

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(e) Graphy=f(x)andy=g(x)and label the point that represents the solution to the equationf(x)=g(x).

Show that the inequality (x-4)2鈮�0has exactly one solution.
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