A B and C in Completing the square?

Question

When I complete the square, and I get this for example:

$$-(x+3)^2 - 13$$

What would $A, B$ and $C$ be? For example, when using $C - B^2 / 4A$

Thanks!

Answer 1

$$-(x+3)^2 - 13=\color{red}{-1}x\color{blue}{-6}x\color{green}{-22}$$
so $A=\color{red}{-1}, B=\color{blue}{-6},C=\color{green}{-22}$ this is what you're looking for?

Answer 2

$-(x+3)^2-13=-(x^2+6x+9)-13=-x^2-6x-22=\color\red{(-1)}x^2+\color\red{(-6)}x+\color\red{(-22)}$

Hence:

• $a=-1$
• $b=-6$
• $c=-22$

Answer 3

Let $(x+a)^2+b=Ax^2+Bx+C$

Then $A=1, B=2a, C=a^2+b$.

In your case we have to watch the signs:

Let $-(x+a)^2-b=Ax^2+Bx+C$

Then $A=-1, B=-2a, C=-a^2-b$.

$A=-1, B=-6, C=-22$