Tricia completed the square of the quadratic function f (x) = x^2+14x+2 and determined the coordinates of the minimum value are (-7,-47). which equation must be Tricia's result? a. f (x) = (x+7) ^2-47 b. f (x) = (x+7) ^2+47 c. f (x) = (x-7) ^2-47 d. f (x) = (x-7) ^2+47

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Mathematics

Pop Tart

3 June, 15:43

Tricia completed the square of the quadratic function f (x) = x^2+14x+2 and determined the coordinates of the minimum value are (-7,-47). which equation must be Tricia's result? a. f (x) = (x+7) ^2-47 b. f (x) = (x+7) ^2+47 c. f (x) = (x-7) ^2-47 d. f (x) = (x-7) ^2+47

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Cristian Bradshaw · Answer 1

To complete the square you halve the coefficient of the x term and square it. Half of 14 is 7 and 7² is 49. So we add 49 and subtract 49, which means we are not changing the value of the quadratic. So we have x²+14x+49-49+2. This can be written: (x²+14x+49) - 49+2, which is (x+7) ²-47, which is answer a.