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Need Help with this question C1 (see attached pic)

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1. this is what i got so far not sure if im correct, cant find this question in any past paper and i dont have the mark scheme either.
y=x^3 [standard graph]
y=f(x-1)+2
f(x-1)+2=(x-1)^3 +2
...
y=x^3-3x^2+3x+1
a=-3 b=3 c=1
This is what im confused about, a the standard y=x^3 graph crosses the x-axis at -2 and 2 but this one crosses at -1 and 2 i don't know how to do this. If someone could explain how i do this it would be great.

2. (Original post by KappaRoss)
...
Method 1:

You need only plug the points given into the equation: - this is equation 1.

- this is equation 2.

The derivative is

You know that there is a maximum (hence zero gradient) at - so

You know that so you then have or .

You can use either of those two equations, they'd get you the same answer.

Method 2:

The best way to do this question would have been to notice that is a root, is a double root (i.e: it doesn't cut the x-axis, it just kinda touches it and bounces off tangentially).

the equation of the cubic is then expand that and find the coefficients.

Method 3:

Alternatively, you could also have gotten and then since , we get two equations:

- equation 1.

- equation 2.

Then solve simultaneously.
3. thank you very much
4. (Original post by KappaRoss)
thank you very much
You're very welcome!

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