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

The co-ordinates which give the minimum value for the quadratic function are (-7, -47)

Step-by-step explanation:

i) the quadratic function f(x) =  + 14x + 2

                                             =  +   14x + 49 - 49 + 2

                                             =     - 49 + 2

                                            =  - 47

ii) The minimum value of the result of the quadratic equation in i) will be achieved when is zero as any square value is always positive and thus the minimum value of a square is always zero.

iii)  is zero when x  = -7 and when x = -7  then y = f(x) = -47

iv) The co-ordinates which give the minimum value for the quadratic function are (-7, -47)