Question

HELP PLEASE ! What is the equation of the parabola in vertex form? x^2+6x-y+3=0

Answer 1

This requires a method called... completing the square... you know of it?

Answer 2

Not really :/

Answer 3

this isnt quite my expertise

Answer 4

ahh completing the square...a lost art

Answer 5

Well, ultimately, your intention is to be able to express your equation in this form...
\[\Large (x-h)^2 +k\]

Answer 6

And how to do that? Well, allow me to present an example :)

Answer 7

please and thank you :D

Answer 8

Okay, suppose we have this...
\[\Large x^2 + {8}x +{7}\]
And we want it in vertex form... well...

Answer 9

There are three numerical parts to this simplified quadratic expression... the coefficient of the square... (here, understood to be 1, since \(x^2\) stands alone)
\[\Large \color{red}1x^2 + {8}x +{7}\]



The coefficient of the linear x (in other words, the coefficient of the x with no exponent)
\[\Large x^2 + \color{blue}{8}x +{7}\]





And the constant...
\[\Large x^2 + {8}x +\color{green}{7}\]


Catch me so far?

Answer 10

Yes i know that stuff lol :D i just cant solve it ;/

Answer 11

Okay. What we're interested in is the coefficient of the linear x.
\[\Large x^2 + \boxed{8}x +{7}\] in this case, 8.


What I want you to do with this, is take half of it, and then square that number...
So, take half of 8, and then square it, what do you get?

Answer 12

4 squared

Answer 13

Which is...?

Answer 14

16 :)

Answer 15

Okay, great. That's the key number we have (along with 4, which is its square root).
So, completing the square involves adding THAT number, but ALSO subtracting it, to keep the expression the same... like so...
\[\Large x^2 + {8}x\color{green}{+16} +{7}\color{red}{-16}\]
Catch me so far?

Answer 16

yes,i wish you would have used the one im trying to solve as an example lol

Answer 17

Yeah...but I wish you'd be able to do your own question yourself, after a really nice example from me :)

Answer 18

prob wont be able to but proceed

Answer 19

You will... you need to believe in yourself, mate :P

Anyway...
You'll notice that this part here..
\[\Large \boxed{x^2 + {8}x + 16} +{7}-16\]
Is now a perfect square.

It IS a perfect square, right? Factor it...

Answer 20

yeah it is

Answer 21

Okay, prove it... express it as the square of some binomial...

Answer 22

lol i cant :p

Answer 23

im telling you ill never understand this stuff

Answer 24

Don't tell me that, that's the same as telling me that there's no point in tutoring you :)

Come on, I believe in you, you can do this... ;)

Answer 25

i can try but i dont even know how to factor equations

Answer 26

Well, that's a problem... read up on "perfect square trinomials"
I'll wait :)

Answer 27

yeahhh i dont understand that x-5 x x-5 all that stuff math is not my thing your very friendly though and thanks for trying :D

Answer 28

Are you giving up? Don't give up yet... you can do this... come on, pick yourself up and try again :)

Answer 29

Its like 3 in the morning where i live tell you what,if you are on here tommorow and i am too earlier i will try to let you tutor me,right now im trying to finish up these quizzes to graduate !

Answer 30

hmm... fair enough.

Answer 31

:)