Why can f(x) = 4x^2 + 4x + 1 not take on values lower than 0.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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