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Why can f(x) = 4x^2 + 4x + 1 not take on values lower than 0.
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The function given is : f(x) = 4x^2 + 4x + 1
4x^2 + 4x + 1
= (2x)^2 + 2*2x*1 + 1^2
= (2x + 1)^2
The function f(x) = 4x^2 + 4x + 1 = (2x + 1)^2. The square of real numbers is always positive and the minimum value it can take on is 0^2 =0.
The function f(x) cannot take on values lower than 0, as the square of negative as well as positive real numbers is positive.
Posted by justaguide on September 23, 2013 at 4:20 AM (Answer #1)
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