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Chapter 2: Q. 75 (page 114)

complete the square of each quadratic expression. Then graph each function using the technique of shifting.

f(x)=x2+2x

Short Answer

Expert verified

The graph of the given equation is

Step by step solution

01

Step 1. Given information

Given expression:

f(x)=x2+2x

02

Step 2. Write the concept

In order to complete the square, we will add or subtract some numbers in order to simplify it

03

Step 3. Calculation

Let's add and subtract 12on right side therefore,

f(x)=x2+2x+12-12=(x+1)2-1

04

Step 4. Graphing using shifting technique

In order to graph the given expression we need to draw the graph of y=x2i.e.

05

Step 5. Graphing the actual expression

Replace x+1by xin the expression

f(x)=x2f(x)=(x+1)2

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

h(x)=12x

The slope of the line containing the points (-2, 3) and (3, 8) is ________.

If 4,2is a point on the graph of y=f(x), which of the following points must be on the graph of y=f2(x)?

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x
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