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Chapter 9: Q.9.120 (page 957)

Graph f(x)=x2鈭�8x+12 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 isfx=x2-8x+12

02

Step 2.  Separate the x term from the constant.   

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

fx=x2-8x+12fx=x2-8x+12

03

Step 3. complete the square   

Now, Take half of 16and then square it, we get:

12路82=16

So, role="math" localid="1645286610146" 16will complete the square.

04

Step 4. Write in the required form  

The constant 16completes the square and then we have to subtract 16from the constant.

role="math" localid="1645286954906" fx=x2-8x+16+12-16fx=x-42-4a-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 right 4unit and down 4units.

The graph of the function after transformations, we get:

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