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Forming an equation for a cubic graph

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1. Part a).

So I concluded that c = 4. Then I tried to do something with like with a parabola - I took the x values to form (x+1)(x-2), but I'm not sure if I'm going the right direction on what to do really.

Any help pls?
2. (Original post by frostyy)
So I concluded that c = 4. Then I tried to do something with like with a parabola - I took the x values to form (x+1)(x-2), but I'm not sure if I'm going the right direction on what to do really.

Any help pls?
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.
3. (Original post by frostyy)
...
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).

Hence the equation of the cubic is then expand that and find the coefficients.
4. (Original post by frostyy)
...
Alternatively, you could also have gotten and then since , we get two equations:

- equation 1.

- equation 2.

Then solve simultaneously.
5. This question is basically seeing if you are aware of how the equation of a function relates to its roots.
A polynomial function with roots can be written as .
A multiple root shows that at that point, the x axis is a tangent to the curve.
A single root shows that the curve crosses the x axis at that point.

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