Question

Tricia completed the square of the quadratic function f(x) = x² + 14x + 2 and determined the coordinates of the minimum value are (-7, -47).

Which equation must be Tricia's result?
f(x) = (x + 7)² + 47
f(x) = (x +7)² - 47
f(x) = (x -7)² + 47
f(x) = (x -7)² - 47

Answer 1

f(x) = (x + 7)² - 47

Explanation:

Given

f(x) = x² + 14x + 2

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 14x

f(x) = x² + 2(7)x + 49 - 49 + 2

= (x + 7)² - 47