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Chapter 9: Q. 9.119 (page 957)

Graph f(x)=x2+2x鈭�3 by using transformations.

Short Answer

Expert verified

The graph of the given function is

Step by step solution

01

Step 1. Given Information  

The given function isf(x)=x2+2x-3

02

Step 2.  Separate the x term from the constant.  

First, separate the xterm from the constant and factor, we get:

fx=x2+2x-3f(x)=x2+2x-3

03

Step 3. complete the square  

Now, Take half of 2and then square it, we get:

12路22=1

So, 1will complete the square.

04

Step 4. Write in the required form  

The constant 1completes the square and then we have to subtract 1from the constant.

role="math" localid="1645284615423" f(x)=x2+2x+1-3-1fx=x+12-4a+b2=a2+2ab+b2

05

Step 5. Graph the function

Looking at the h, k values, we see the graph will take the graph of fx=x2and shift it to the left 1unit and down 4units.

The graph of the function after transformations, we get:

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