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Chapter 9: Q. 9.117 (page 956)

Rewrite f(x)=鈭�4x2鈭�8x+1in the localid="1645190772677" f(x)=a(x鈭�h)2+kform by completing the square.

Short Answer

Expert verified

Thefx=ax-h2+kform of the given function islocalid="1645190703166" fx=-4x+12+5

Step by step solution

01

Step 1. Given Information

The given function isfx=-4x2-8x+1

02

Step 2. Separate the x term from the constant.

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

-4x2-8x+1=0-4x2+2x+1=0

03

Step 3. complete the square

Now, Take half of2and then square it, we get:

localid="1645118255707" 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 -4脳1=-4from the constant.

fx=-4x2+2x+1+1-(-4)fx=-4x+12+5a+b2=a2+2ab+b2

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