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Hassnain Ali Rashid
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(@hrashid_)
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Can someone please explain Question 4b, 5a and 5b

Gracias 

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Leanorad
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@hrashid_

When you have an expression in brackets, then that bracket has a power, it works like the following:

(2x^3)^3 = 2^3x^{3*3}

So as you can see, the power times everything in the brackets. So similarly if you have:

x(2x^{\frac{-1}{3}})^4

Focus on the (2x^{\frac{-1}{3}})^4

Simplify that, then times it by x

As for question 5,

imagine if  y = 2x^5

And they said work out  y^3

They basically mean just work out  (2x^5)^3

Which is just  2^{3}x^{15}

So similarly, try the same thing.

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Lillie Roper
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Please could someone help me with how to find the line of symmetry after completing the square. Any help would be greatly appreciated:)聽

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Further_Maths_Student
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@lilyy

When you complete the square, you have the line of symmetry

say for example you had a quadratic and you completed the square and you got:

(x- 5)^2 +聽 3

Do you know what the minimum point of this quadratic would be?

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Further_Maths_Student
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just fixed the expression

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Lillie Roper
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@further_maths_student Yess I know how to get the minimum point, is it just the X value of the minimum point? Xx

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Further_Maths_Student
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@lilyy

Yeah, literally

image

 

so this line of symmetry would just be the minimum point x = 5 

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Lillie Roper
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@further_maths_student ahh Thankyou, and is it the same if there’s a coefficient of x squared??xx

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Zeeshan Ahmed
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@lilyy

Yeah x squared coefficients make no difference - its always the minimum or maximum point

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Lillie Roper
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@zeeshan Thankyouu, you’re a legend 馃檪 

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Hassnain Ali Rashid
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Can someone help me with question 7. Im so baffed.

Thanks

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omkark
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@hrashid_

You need to pretend like they're quadratics

I'll do the first one for you

x^6 + 9x^3 + 8

If you want to make that look like a quadratic (clearly its not right now) you need to pretend x^3 = y

This will make the expression above turn into

y^2 + 9y + 8 which looks much more like a quadratic now

(as y^2 = x^6)

Then you just solve y^2 + 9y + 8 = 0

(y + 8)(y + 1) = 0

y = -8, y = -1

But remember earlier we said x^3 = y

So really 

x^3 = -8, x^3 = -1

so x = -2, x = -1

Finished

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