The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Completing Square

So say I had this:
x^2 + 8x +3
(x + 4)^2 -16 +3
(x + 4)^2 -13
Therefore, the minimum point is (-4,-13)

What if the coefficient was a minus:
-3x^2 + 5x + 5

What would be the minimum points then?
Reply 1
Avatar for Neevan
Neevan
1
= -3(x-5/6)^2 + 85/12
Minimum point = (5/6, 85/12)
Reply 2
Avatar for Nieveee
Nieveee
OP
Original post by Neevan
= -3(x-5/6)^2 + 85/12
Minimum point = (5/6, 85/12)



Thank you so much!!! So regardless of the minus, the x coordinate of the minimum point will be positive and not timesed by 3? It's basically never affected by the coefficient right...oh and the y as well for that matter?
Original post by Nieveee
So say I had this:
x^2 + 8x +3
(x + 4)^2 -16 +3
(x + 4)^2 -13
Therefore, the minimum point is (-4,-13)

What if the coefficient was a minus:
-3x^2 + 5x + 5

What would be the minimum points then?


It won't be a minimum though will it?

What shape is a quadratic with a negative x^2 coefficient?
Reply 4
Avatar for Nieveee
Nieveee
OP
Original post by Muttley79
It won't be a minimum though will it?

What shape is a quadratic with a negative x^2 coefficient?


Ahhh, it'd be a maximum right, considering it's the other way round?
Original post by Nieveee
Ahhh, it'd be a maximum right, considering it's the other way round?


Indeed :smile:
Reply 6
Avatar for Neevan
Neevan
1
sorry about that
Reply 7
Avatar for Nieveee
Nieveee
OP
Original post by Muttley79
Indeed :smile:

Oh, so would I be right in saying the maximum of this is, for example:

-2(x-2)^2 + 18
= (2,18)

and this:
4(x-3)^2 + 23
= (3, 23) is the minimum point?
Reply 8
Avatar for Nieveee
Nieveee
OP
Original post by Neevan
sorry about that

No problem! :smile:
Original post by Nieveee
Oh, so would I be right in saying the maximum of this is, for example:

-2(x-2)^2 + 18
= (2,18)

and this:
4(x-3)^2 + 23
= (3, 23) is the minimum point?


Yes - remember you can always check by differentiating and putting dy/dx =0 if you have time.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you