Express 9x^2 - 36x + 52 in the form (Ax-B)^2 +C .Hence,find the set of values taken by 9x^2 -36x + 52 for x€R

Question

A ,B and C are integers and 'x€R' means that x is an element of real numbers

Answer 1

9x² - 36x + 52 = 9(x²-4x) + 52

 

                       = 9(x²-4x+4) - 36 + 52

 

                       = 9(x-2)² + 16

 

                       = [3(x-2)]² + 16

 

                       = (3x-6)² + 16

 

(3x-6)² ≥ 0 for all x

 

So, (3x-6)² + 16 ≥ 16 for all x.  

 

9x² - 36x + 52 takes on all values greater than or equal to 16.