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OCR Maths Question

what our maths teacher learnt us confuses this question loads so can anyone tell me if im right..thanks

if u complete the square on a question n say come out with:

(x - 4)² - 19

Does this mean that the:

Minimum Value = -19
and
Minimum Point = (4,-19)

Thanks i keep being told im wrong for the minimum value one but im sure im not.
Reply 1
Avatar for RedDevils
RedDevils
OP
3
Doesn't anyone know? :frown:
I have an idea about it, but could you write down the whole question please?
Reply 3
Avatar for RedDevils
RedDevils
OP
3
Its just a typical question...you complete the square in part:

i) Write y = x² - 8x - 3 in the form y = (x - a)² + b

and the answer is:

(x - 4)² - 19

ii) Hence find the minimum value of y = x² - 8x - 3.

I think the answer is -19
Reply 4
Avatar for henryt
henryt
17
Yes. It is -19. The way to think about it is that the (x-4)^2 must either be 0 or positive. As a result, the minimum value is going to be when the bracket equals 0 (i.e. when x=4). So the minimum value is -19, and the minimum point is (4,-19). Does that make sense? Hope so :smile:
Reply 5
Avatar for RedDevils
RedDevils
OP
3
Haha i knew it , yeah thanks i always thought it was but i was told putting -19 for the minimum value was wrong!!
Reply 6
Avatar for NesQuiK.
NesQuiK.
13
hi, so will the minimun value always be the -19 or whatever number taht comes after the bracket, what if the -19 was +19?
Could somebody also explain how we get the minium point im just abit confised about the the +4 came from?

thanks
Reply 7
Avatar for Creole
Creole
2
In the form:

a(x+b)2+ca(x+b)^2+c

The minimum point will always be (−b,c)(-b,c).

For example:

Find the minimum point of the curve y=2x2−4x+4y=2x^2-4x+4

First take a factor of 2 out to factorise it.

y=2(x2−2x+2)y=2(x^2-2x+2)

Then complete the square:

y=2((x−1)2−1+2)y=2((x-1)^2-1+2)

Then tidy it up:

y=2((x−1)2+1)y=2((x-1)^2+1)

y=2(x−1)2+2y=2(x-1)^2+2

Therefore the minimum point is (1,2).

Hope this clears up any confusion.
Reply 8
Avatar for Leonidas
Leonidas
Great explanation!
Reply 9
Avatar for abbs_aly
abbs_aly
Yep very nice! Can any1 explain da stretch/compression of parables please. Always a question on them!
Reply 10
Avatar for abbs_aly
abbs_aly
any1.....
Reply 11
Avatar for warrior-1
warrior-1
2
abbs_aly
Yep very nice! Can any1 explain da stretch/compression of parables please. Always a question on them!



You mean transformations?? They are easy- jus couple of rules, check in ur text book

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