+586 The quadratic 4/3x^2+4x+1 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is abc? Give your answer in simplest form.
+128474 (4/3)x^2 + 4x + 1 factor out the 4/3
(4/3) [ x^2 + 3x + 3/4 ] complete the square on the quadratic inside the brackets
(4/3) [ x^2 + 3x + 9/4 + 3/4 - 9/4 ] factor the first three terms and simplify the rest
(4/3) [ (x + 3/2)^2 - 3/2 ] distribute the (4/3) over the terms
(4/3) ( x + 3/2)^2 - 2 = (4/3) ( x + 3/2)^2 + (-2)
So...in the form a( x +b)^2 + c
a = (4/3) b = (3/2) and c = -2
So
abc = ( 4/3)(3/2)(-2) = -24 / 6 = -4
