Question

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

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.