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Chapter 9: Q. 9.118 (page 956)

Rewrite (x)=2x2鈭�8x+3 in the f(x)=a(x鈭�h)2+k form by completing the square.

Short Answer

Expert verified

The ax-h2+kform of the given function isfx=2x-22-5

Step by step solution

01

Step 1. Given Information 

The given function isfx=2x2-8x+3.

02

Step 2.  Separate the x term from the constant. 

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

fx=2x2-8x+3fx=2x2-4x+3

03

Step 3. complete the square 

Now, Take half of 4and then square it, we get:

12路42=4

So,4will complete the square.

04

Step 4. Write in the required form 

The constant 4completes the square and then we have to subtract 2脳4=8from the constant.

fx=2x2-4x+4+3-8fx=2x-22-5a-b2=a2-2ab+b2

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