+816 The quadratic \(-x^2+2x-4\)can be written in the form \(a(x+b)^2+c\), where a, b, and b are constants. What is a+b+c?
+128407 -x^2 + 2x - 4 let us complete the square....factor out a "-1" and we have
- ( x^2 - 2x + 4) take 1/2 of -2 = -1, square it = 1...add and subtract it inside the parentheses
- ( x^2 - 2x + 1 + 4 - 1) factor the first three terms, simplify the rest
- [ ( x - 1)^2 + 3 ) apply the ngative back across the terms
- ( x - 1)^2 -3
"a" = -1
"b" = -1
"c" = -3
So
a + b + c = -1 + -1 + -3 = -5
