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Knowing which equation to use for graph functions

Hello,
Please see this recent post as I am having the same problem: http://www.thestudentroom.co.uk/showthread.php?t=697766

It is taken from the Edexcel Core Mathematics book, which does not explain which equation to use for the following problem. Just wondering how can one know which equation to use. A poster suggested to use k(x-a)(x-b) for the equation for the graph.

Please could you provide me with more information as I have stated this is what is missing from the book and if I hadn't stumbled accross this post I would be stuck.

Thanks
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Avatar for dthomas86
dthomas86
OP
3
Ok if someone please could check my method with what I have got so far:

The graph cuts the x-axis at 1 and 3

Therefore y=(1+x) and y=(3+x)
So x= -1 ad x=-3

f(x)=(x-1)(x-3)

Expand the brackets:

f(x)=x^2-4x+3

And thats the equation for the given diagram?

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