The quadratic -6x^2 + 30x - 216 can be written in the form a(x + b)^2 + c, where a, b, and c are constants. What is a+b+c?
+128475 -6x^2 + 30x - 216 factor out the -6
-6 (x^2 - 5x + 36) complete the square on x
Take 1/2 of 5 = 5/2......square it = 25/4 add and subtract this within the parentheses
-6 ( x^2 - 5x + 25/4 + 36 - 25/4) factor the first three terms....simplify the rest
-6 [ (x - 5/2)^2 + 119/4 ] distribute the -6 acroos the terms in the brackets
-6 (x -5/2)^2 -357/2
a = -6 b = -5/2 c = -357/2
a + b + c = - (12/2 + 5/2 + 357/2) = - (374/2) = -187
