The method of compleating the square can be used to write the expression -3x^2+8x-2 in the form a(x+b)^2+c,where a,b,and c are constants. Choose the option that gives the value of c.
A -22/3 , B -10/9 , C -2/9 , D 2/3 , E 14/9 or F 10/3

Question

The method of compleating the square can be used to write the expression -3x^2+8x-2 in the form a(x+b)^2+c,where a,b,and c are  constants. Choose the option that gives the value of c.
A -22/3 , B -10/9 , C -2/9 , D 2/3 , E 14/9 or F 10/3

anonymous · Answer

$$-3x^2 + 8x - 2 = a(x + b)^2 + c$$$$-3x^2 + 8x - 2 = a(x^2 + 2bx + b^2) + c$$$$-3x^2 + 8x - 2 = ax^2 + 2abx + ab^2 + c$$equate the coefficients
$$a = -3$$$$2ab = 8$$$$ab^2 + c = -2$$after that solve for c