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completing the square

im on the last step of completing the square when a>1

when multiplying 2 with everything, where did the denominator go from 15/2?and if the denominator was not a 2, let's say it was 15/10, then would that become 15/5? is my logic right or am i missing something

Reply 1

fatima1998

its dominator gets divided so 2/2=1 :unsure:

Reply 2

1420787

The 2 at the front is to multiply everything. So 2 x 15/2 = 15.

But you're learning how to do this by working from the marking scheme?

Reply 3

TSR George

Original post by offhegoes

The 2 at the front is to multiply everything. So 2 x 15/2 = 15.

But you're learning how to do this by working from the marking scheme?

no im learning C1 and C2 from the wjec revision and study guide along with my notes from the step-up classes and youtube videos and TSR xD

Reply 4

B_9710

If you have a general quadratic

\displaystyle ax^2 + bx + c

when completing the square you get

\displaystyle a(x^2+\frac{b}{a}x) + c \equiv a \left (x^2+\frac{b}{2a} \right )^2 + c- \frac{b^2}{4a}

.
So if you have

y=2x^2+8x+10

you complete the square as follows

y=2(x^2+4x)+10 \Rightarrow y=2(x+2)^2+10 -2(4)

.
You multiply the 4 by 2 as there is a 2 out front to the left of the brackets.

(edited 7 years ago)

Reply 5

TSR George

Original post by fatima1998

its dominator gets divided so 2/2=1 :unsure:

i see, im not used to multiplying out like this :redface:

never seen anything like it at gcse :cry:

Reply 6

RDKGames

Study Forum Helper

I mean... you kinda double 15 halves... that's like doubling a halve, then multiplying that 15 times....

When you multiply everything by 2, the 15/2 goes to (15x2)/2 where the 2's cancel. Surely you should know this without question?

(edited 7 years ago)

Reply 7

fatima1998

OMGGGG its GCSEs that means i still can do it :ahee:

its just like you 2*15/2

Reply 8

1420787

2 x 15/2....

Trying writing 2 as 2/1.

So this becomes 2/1 x 15/2

Top times top over bottom times bottom. Try cross-cancelling first to see why the 2 disappears though.

So many pupils of your level have such poor fraction skills! (No offence, just an observation).

Reply 9

RDKGames

Study Forum Helper

Original post by offhegoes

I'm more surprised by the "never seen anything like it at gcse".. I've done my GCSE's just over 2 years ago and this should be common knowledge, shouldn't it? I'm pretty sure pupils are expected to multiply fractions in one way or another.

Reply 10

TSR George

Original post by offhegoes

i know, fractions scare me, especially those equations

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i had a question similar to this in my gcse and i was all over the place, to this day i still dont know how you would solve these things, like what do you do with the 31/6 denominator???

Original post by RDKGames

i understand it now that you've written it like (15x2)/2, because in my head i saw it as (15x2)/(2x2) :redface:

Reply 11

RDKGames

Study Forum Helper

I see. When multiplying a fraction by an integer, only the numerator gets multiplied. When a fraction is multiplied by a fraction, the numerators and denominators multiply respectively.

However if you add fractions, you want to get them under the same denominator in which case you are free to combine them. In the example you posted, you only need to multiply the first term by 3 (top and bottom) and the second by 2. The reason behind multiplying numerator AND denominator is so you can preserve the equality of the quantity (or keep the value of the expression the same), while maintaining a different denominator. Now you have everything over 6 at which point you just multiply throughout by 6 which makes the fractions cancel and then you're dealing with a simple linear equation.

Once you get better, you'll just realise that you can simply multiply the whole equation by 6. As 2 and 3 are factors of 6, they will go away and you will be left with no different denominators.