write in the form (x+a)^2+b

srose

Hi
How do I do this question:
write f(x) = x^2+6x+11 in the form (x+a)^2+b

Thanks

Reply 1

Tibbles168

Complete the square, if you still don't get it, I'll give you a clue later.

Reply 2

Willis123

complete the square.

take the form x^2+ax+b

complete the square will become (x+.5a)^2-(.5a)^+b

Reply 3

Necro Defain

Here's an example: x^2 + 8x + 13 becomes (x+4)^2 - 16 + 13 = (x+4)^2 - 3, can you do it now? :smile:

Reply 4

xsinfinity

You need to complete the square.

Reply 5

+epic

srose

Hi
How do I do this question:
write f(x) = x^2+6x+11 in the form (x+a)^2+b

Thanks

By completing the square...
So you go (x+3)^2-9+11
then (x+3)^2+2 ---------> so a=3 and b=2

so the answer is x= -3 and 2.

Reply 6

username165864

Use the general formula:

x^2 + ax + b \equiv (x+\frac{a}{2})^2 - \frac{a^2}{4} + b

Reply 7

srose

Thanks for the replies.

I understand everything apart from where the -9 comes from in:

(x+3)^2-9+11

Reply 8

COMMUNIST

f(x) = x^2+6x+11

Halve the

6x

to get 3 and shove it in the brackets

(x+3)

Now SQUARE 3 and put it outside the brackets. It must always be minus.

Therefore

(x+3)^2 -9

and don't forget the rest of the equation:

(x+3)^2 -9 +11

becomes

(x+3)^2 +2

You need to use a different method when the coefficient of

x^2 > 1

Follow the example of the formula given a few posts above and you should be fine.

Reply 9

srose

Ok, Thanks I get it now

Reply 10

sam161

Mathematician!

Use the general formula:

x^2 + ax + b \equiv (x+\frac{a}{2})^2 - \frac{a^2}{4} + b

\frac{a^2}{4}

I thought it was just

a^2

Reply 11

COMMUNIST

sam161

\frac{a^2}{4}

I thought it was just

a^2

It may not always be a whole number.

E.g

x^2 -3x +4

(x-\frac{3}{2})^2 - (\frac{3}{2})^2 +4

(x-\frac{3}{2})^2 - \frac{9}{4} + 4

Reply 12

username219321

Look up completing the square

Reply 13

heuygff

how do u square it?
where did u get 3 and the nine from. they werent even in the ques!
and if it was x^2 - 8x + 21, what wud the answer be?

Reply 14

Super199

Original post by heuygff

how do u square it?
where did u get 3 and the nine from. they werent even in the ques!
and if it was x^2 - 8x + 21, what wud the answer be?

Bumping a thread that is over 4 years old :eek:

Thanks very much!

Like thats gonna help no offence but this is a topic im personally struggling on and id prefer if u went itno more depth... btw sorry im not trying to be rude ,maths isnt my strong subject

Reply 17

Dysf(x)al

Original post by ............d

Like thats gonna help no offence but this is a topic im personally struggling on and id prefer if u went itno more depth... btw sorry im not trying to be rude ,maths isnt my strong subject