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# Maths (sketching a curve) watch

1. Sketching a curve using the following cubic function:
(just finding out the y-intercept and the x-intercept here)

$f(x)=(x-3)^2(x+1)$

Y-Intercept:

Let x = 0

$(x-3)^2(x+1)$

$(0-3)^2(0+1)$

$(-3)^2(1)$

$(-3)^2$

$9$

Y-Intercept = 9

X-Intercept:

Let f(x) = 0

$(x-3)^2(x+1)=0$

$(3-3)^2=0$

$(-1+1)=0$

X-Intercept = 3 or -1

Am I correct?
2. You're all correct there as far as I can see, but it is worth noting the importance of the squared (x-3) term. This means that the x axis is a tangent to the curve at the root x=3. This is very important when sketching and although you could differentiate to find the turning points and see this anyway, it's much easier to just recognise it straight away. With this information, and the other root and the general shape of a cubic, you can't go far wrong.
3. (Original post by B_9710)
You're all correct there as far as I can see, but it is worth noting the importance of the squared (x-3) term. This means that the x axis is a tangent to the curve at the root x=3. This is very important when sketching and although you could differentiate to find the turning points and see this anyway, it's much easier to just recognise it straight away. With this information, and the other root and the general shape of a cubic, you can't go far wrong.
Yeah I know about the importance of the (x-3)^2. Since the cubic has a double root (which is x=3) it would mean when sketching the curve should only barely touch x=3, instead of going through it.
4. (Original post by Aklaol)
Yeah I know about the importance of the (x-3)^2. Since the cubic has a double root (which is x=3) it would mean when sketching the curve should only barely touch x=3, instead of going through it.
Yes, although I wouldn't say barely touch, since when we say touch we mean it in quite an exact way, but yeah.
5. (Original post by B_9710)
Yes, although I wouldn't say barely touch, since when we say touch we mean it in quite an exact way, but yeah.
True, I just said barely touching to emphasise on the fact that the curve shouldn't go through x=3.
6. (Original post by Aklaol)
True, I just said barely touching to emphasise on the fact that the curve shouldn't go through x=3.
I know I'm just being pedantic.

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