# Quadratics MEP1 7 (b)

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IFoundWonderland

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#1

7. (A) Write x

I got (x-5)

7. (B) Hence, or otherwiwe, find the maximum value of 1/(x

My problems:

Tf is this asking? The value of x that will make the fraction largest? Surely lowest possible value of x?

Isn't it possible for negative infinity to satisfy this?

^{2}-10x+35 in the form (x-p)^{2}+q.I got (x-5)

^{2}+10=07. (B) Hence, or otherwiwe, find the maximum value of 1/(x

^{2}-10x+35)^{3}.My problems:

Tf is this asking? The value of x that will make the fraction largest? Surely lowest possible value of x?

Isn't it possible for negative infinity to satisfy this?

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Zacken

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(Original post by

7. (A) Write x

I got (x-5)

**IFoundWonderland**)7. (A) Write x

^{2}-10x+35 in the form (x-p)^{2}+q.I got (x-5)

^{2}+10=0The reason this is so is because squares are

**always positive. (**or zero). That is, if I take a number, whatever number I can think of and square it, I'll get a number that is .

So - for example, let's say I pick , well then , squares are always positive.

So when you write a quadratic in the form you know that the smallest possible value of this entire expression is when the squared bracket is 0 - 'cause you can't make a squared brackets smaller than 0.

So for any possible value of you can think of - and that means for any value you can think of.

Which is basically saying that the minimum point occurs at the point (where the squared bracket becomes 0, y coordinate of that point).

The squared bracket is zero precisely when , so the minimum point of this quadratic is at Any other value of x will give you a y-coordinate bigger than 10.

Like, let's say then so the y coordinate is .

The graph of the quadratic looks like this:

So as you can see, the graph is always bigger than 10. (you might want to sketch this in your gdc in the calculator to appreciate it and understand it in the exam).

7. (B) Hence, or otherwiwe, find the maximum value of 1/(x

My problems:

Tf is this asking? The value of x that will make the fraction largest? Surely lowest possible value of x?

Isn't it possible for negative infinity to satisfy this?

^{2}-10x+35)^{3}.My problems:

Tf is this asking? The value of x that will make the fraction largest? Surely lowest possible value of x?

Isn't it possible for negative infinity to satisfy this?

To make the denominator the smallest, you want to make the bit inside the bracket the smallest, because smallest^3 = smallest.

That is - we want to make as small as possible and we showed that the smallest possible value of this is 10. If I put x = -infinity, I end up squaring that -infinity and getting +

**infinity^2.**Which is just bad for our health.

So, yeah, the smallest value of the bracket is 10 - the smallest value of the bracket cubed is 10^3.

So the biggest value of the fraction is 1/(10^3).

Hope that makes sense, let me know if I need to explain anything anymore!

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IFoundWonderland

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Zacken

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IFoundWonderland

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#5

(Original post by

Yasss! Awesome.

If you want to read more of my ramblings on how completing the square works (including a pretty gif) you can see here and here; but I reckon you've got it down pat.

**Zacken**)Yasss! Awesome.

If you want to read more of my ramblings on how completing the square works (including a pretty gif) you can see here and here; but I reckon you've got it down pat.

How do I do this? 😓

At first I tried using the quadratic formula; then attempted to put it into the completed square form (to no avail)....

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username2412509

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#6

**Zacken**)

Yasss! Awesome.

If you want to read more of my ramblings on how completing the square works (including a pretty gif) you can see here and here; but I reckon you've got it down pat.

(Original post by

Sorry to bother you for the fifty millionth time...

How do I do this? 😓

At first I tried using the quadratic formula; then attempted to put it into the completed square form (to no avail)....

**IFoundWonderland**)Sorry to bother you for the fifty millionth time...

How do I do this? 😓

At first I tried using the quadratic formula; then attempted to put it into the completed square form (to no avail)....

(it's ethereal world btw)

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Zacken

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#7

(Original post by

How do I do this? 😓

**IFoundWonderland**)How do I do this? 😓

- now you can just compare coefficients - can you take it from there?

Edit to add: whenever a question starts with "let be roots..." then this particular approach should come to mind straightaway.

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#8

(Original post by

If and are roots - then you should be able to write the quadratic in the form:

- now you can just compare coefficients - can you take it from there?

Edit to add: whenever a question starts with "let be roots..." then this particular approach should come to mind straightaway.

**Zacken**)If and are roots - then you should be able to write the quadratic in the form:

- now you can just compare coefficients - can you take it from there?

Edit to add: whenever a question starts with "let be roots..." then this particular approach should come to mind straightaway.

(Original post by

This is so cute! I love how helpful Zacken is. Wonderland, when Zacken moves to the UK for university, shall we go to Cambridge and treat him to dinner for how amazing he is?

(it's ethereal world btw)

**Freudian Slit**)This is so cute! I love how helpful Zacken is. Wonderland, when Zacken moves to the UK for university, shall we go to Cambridge and treat him to dinner for how amazing he is?

(it's ethereal world btw)

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stochasym

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#10

(Original post by

You make it seem so simple -_-

**IFoundWonderland**)You make it seem so simple -_-

You had:

All you need to do is notice that .

Note that when you expand which you've mixed up.

Then from there on, it simplifies down to so you get .

Sorry - you were actually on the right track, just a sign error - ignore what I said previous about comparing coefficients, let's focus on the method you already know.

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#11

(Original post by

Yours is actually simpler - you were right on track with the quadratic formula.

You had:

All you need to do is notice that - note that when you expand .

Then from there on, it simplifies down to so you get .

Sorry - you were actually on the right track, just a sign error - ignore what I said previous about comparing coefficients, let's focus on the method you already know.

**Zacken**)Yours is actually simpler - you were right on track with the quadratic formula.

You had:

All you need to do is notice that - note that when you expand .

Then from there on, it simplifies down to so you get .

Sorry - you were actually on the right track, just a sign error - ignore what I said previous about comparing coefficients, let's focus on the method you already know.

I don't understand why the 4 is allowed to just disappear?

If you have k^2-4k-4, this simplifies to (k-2)^2-8 ; I don't understand where the 8 vanishes to?

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#12

(Original post by

Hey, sorry

I don't understand why the 4 is allowed to just disappear?

If you have k^2-4k-4, this simplifies to (k-2)^2-8 ; I don't understand where the 8 vanishes to?

**IFoundWonderland**)Hey, sorry

I don't understand why the 4 is allowed to just disappear?

If you have k^2-4k-4, this simplifies to (k-2)^2-8 ; I don't understand where the 8 vanishes to?

**- 4.**You have k^2 - 4k

**+ 4.**

When you expand you get .

Just like with and not .

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#13

(Original post by

The thing is you don't have k^2 - 4k

When you expand you get .

Just like with and not .

**Zacken**)The thing is you don't have k^2 - 4k

**- 4.**You have k^2 - 4k**+ 4.**When you expand you get .

Just like with and not .

IT'S DIFFERENCE OF TWO SQUARES 🙄🙄🙄😂😂😂

Thanks man 👊

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#14

(Original post by

OH **** MY LIFE

IT'S DIFFERENCE OF TWO SQUARES 🙄🙄🙄😂😂😂

Thanks man 👊

**IFoundWonderland**)OH **** MY LIFE

IT'S DIFFERENCE OF TWO SQUARES 🙄🙄🙄😂😂😂

Thanks man 👊

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#15

(Original post by

No problem! Do you get the end answer now? You should find or , so those are your roots.

**Zacken**)No problem! Do you get the end answer now? You should find or , so those are your roots.

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#16

(Original post by

I absolutely do thanks for all your help

**IFoundWonderland**)I absolutely do thanks for all your help

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#17

(Original post by

No worries. Is your exam soon?

**Zacken**)No worries. Is your exam soon?

My slip ups tend to be on small things like signs etc, so hopefully I'll iron those out and the exam will be ok.

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#18

(Original post by

Next Tuesday and Wednesday

My slip ups tend to be on small things like signs etc, so hopefully I'll iron those out and the exam will be ok.

**IFoundWonderland**)Next Tuesday and Wednesday

My slip ups tend to be on small things like signs etc, so hopefully I'll iron those out and the exam will be ok.

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