The quadratic -6x^2+72x+216 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?
+2666 Note that \((x+b)^2 = x^2 + b^2 + 2xb\)
This means that \(a = -6\)
Also, note that \(-6 \times 2xb = 72x\), because it is the only term with x.
This means \(b = -6\)
Expanding what we have gives us: \(-6x^2 + 72x -216\), so we add 432, to make the constant positive.
This means \(a + b + c = \color{brown}\boxed{420}\)
+2666 Note that \((x+b)^2 = x^2 + b^2 + 2xb\)
This means that \(a = -6\)
Also, note that \(-6 \times 2xb = 72x\), because it is the only term with x.
This means \(b = -6\)
Expanding what we have gives us: \(-6x^2 + 72x -216\), so we add 432, to make the constant positive.
This means \(a + b + c = \color{brown}\boxed{420}\)
