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Chapter 2: Q. 61 (page 103)

Exploration Graph y=x2. Then on the same screen graph y=(x-2)2, followed by y=(x-4)2, followed by y=(x+2)2. What pattern do you observe? Can you predict the graph of y=(x+4)2 Of y=(x-5)2?$

Short Answer

Expert verified

The graph is and the graph is

Step by step solution

01

Given information

Given the equationy=x2y=(x-2)2y=(x+2)2

02

Sketching the graph

The graph is

03

Checking the graph 

Here all graphs are similar to graph y=x2, shifting by kunits left or right.

Hence, the graph y=(x-5)2can be obtained by shifting the graph y=x2by 5units to right and graph y=(x+4)2can be obtained by shifting the graph y=x2by 4units to left.

04

Sketching the graph

The graph is

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Most popular questions from this chapter

In Problems 19-26,write the function whose graph is the graph of y=x3but is:

Shifted to the left 4units

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.

f(x)=x2+4

True or False Every relation is a function.

Exploration Graph y=x2,y=x4, and y=x6 on the same screen. What do you notice is the same about each graph? What do you notice that is different?

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
See all solutions

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