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f(x) = 0.5x-6x +21 %3D = 0.5(x²-12x+42) = 0.5(x²-12x+ 0.5((x-6)²+6) 0.5(x-6)2 + 3 %3D 36-36 +42) %3D = D. %3D

f(x) = 0.5x-6x +21 %3D = 0.5(x²-12x+42) = 0.5(x²-12x+ 0.5((x-6)²+6) 0.5(x-6)2 + 3 %3D 36-36 +42) %3D = D. %3D

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Quadratic function into vertex form

image is from the teaching video, I do not understand how he gets =36 -36 in the third line

(A) f(x) = 0.5x-6x+21 经) -12 3D36 0.5(x²-12x +42) 0.5(x-12x+36-36+42.) = 0.5((x-c)²+ 6) 0.5((x-6)²+6) 0.5(x-6) 3. %3D %3D %3D %3D
Transcribed Image Text:(A) f(x) = 0.5x-6x+21 经) -12 3D36 0.5(x²-12x +42) 0.5(x-12x+36-36+42.) = 0.5((x-c)²+ 6) 0.5((x-6)²+6) 0.5(x-6) 3. %3D %3D %3D %3D
Expert Solution
Step 1

f(x)=0.5x2-6x+21       =0.5x2-12x+42

Now to do a complete square we need to add and subtract some constant and that constant is given by:

(1) the coefficient of x is -12,

(2) divide the coefficient by 2 ⇒-122=-6 ,

(3) now take a square of that number ⇒(-6)2=36

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