Question

Complete the square, I'm stuck on a step
f(x)=-2x^2+12x-8
Then that changes to -2(x^2-6x+9)-8+18
Is it a +18, or -18?

Answer 1

Plus 18,
you need to apply the -2 to your -18 when you pull it out of the brackets.

Answer 2

\[\Large\rm -2x^2+12x-8\]\[\Large\rm =-2(x^2-6x)-8\]Looks like +9 is what completes the square for us:\[\Large\rm =-2(\color{orangered}{x^2-6x+9}-9)-8\]We subtract 9 at the same time, to keep things balanced.
We want to take the -9 out of the brackets, away from our perfect square.
So we apply the -2 to it when we take it out.\[\Large\rm =-2(\color{orangered}{x^2-6x+9})-8+18\]I'm assuming that's what you were trying to do, yes? :)

Answer 3

My first response:
`you need to apply the -2 to your -18 when you pull it out of the brackets.`

Should have read:
`you need to apply the -2 to your -9 when you pull it out of the brackets.`

Answer 4

On my teacher's answer key at the end she has -8-18, so is that incorrect?

Answer 5

Lemme double check my work just to make sure c:

Answer 6

Yah looks like the teacher made a boo boo,
it happens :3

Answer 7

\[\Large\rm -2x^2+12x-8\quad=\quad -2(x-3)^2+10\]

Answer 8

Thank you