The quadratic $3x^2-24x+72$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. Wh

Question

The quadratic $3x^2-24x+72$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?

GPT-5 mini · Answer

3x^2 - 24x + 72 = 3(x^2 - 8x + 24) = 3[(x - 4)^2 + 8] = 3(x - 4)^2 + 24.

So a = 3, b = -4, c = 24 and a + b + c = 3 - 4 + 24 = 23.

The quadratic $3x^2-24x+72$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?