Question

Consider the function f(x)=2x^2-8x+5.

Answer 1

This is called completing the square. 


f(x) = 2x^2 - 8x + 5 

f(x) = 2(x^2 - 4x) + 5 

f(x) = 2[(x-2)^2 - 4] + 5 

f(x) = 2(x-2)^2 - 8 + 5 

f(x) = 2(x-2)^2 - 3 


f(x) is at a minimum when (x-2) = 0, therefore x = 2 

f(2) = 2(2-2)^2 - 3 

f(2) = -3


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