Need help for methods assignement

[Over9000]

I am having trouble with question 2d.
Can someone show me a proof?

[bigtick]

It must be an inverted parabola. The part smoothly joined to A is defined for x < -3. Clearly it does not pass through D (14, -126).

[Over9000]

Yeh but the inverted parabola doesnt satisfy smooth join, it makes an elbow, I asked my teacher and he said smooth join means must continue.

[bigtick]

The parabola is y = (-192/17)x^2 + (2112/17)x + 5922/17, x < -3.

[Over9000]

Yeh, I got that, the tricky part is, it says must prove cant have a smooth join, so how do I prove that the parabola doesnt smoothly join (i.e how to I prove it elbows?)
The proof must be rigourous also otherwise they might not allocate full marks

[bigtick]

You misunderstood the question!

[Over9000]

You misunderstood the question!

What do you mean? Please explain

[bigtick]

It is rigorous enough. Further explanation is unnecessary.

[Over9000]

So saying parabola equation is The parabola is y = (-192/17)x^2 + (2112/17)x + 5922/17, x < -3.
is enough for an assignment question?

[bigtick]

The question asked you to show that there is no parabola that meets both requirements, smoothly joined to A AND passing through D.

You can find a parabola that is NOT smoothly joined to A but passes through D.

[Over9000]

The question asked you to show that there is no parabola that meets both requirements, smoothly joined to A AND passing through D.

You can find a parabola that is NOT smoothly joined to A but passes through D.

I know but how do you explain algebraically that it isnt a smooth join, if you just put the equation as your answer how would teachers know that that implies it isnt a smooth join. You can just sketch a graph of both and show that the inverted parabola elbows but how do u prove it with algebra instead of just saying by inspection it isnt a smooth join?

[bigtick]

In fact it can be an inverted parabola or a 'normal' parabola.
The part smoothly joined to A is defined for x < -3. Clearly it does not pass through D (14, -126).

[Over9000]

Say what I said.
It must be an inverted parabola.
The part smoothly joined to A is defined for x < -3. Clearly it does not pass through D (14, -126).

Im not quite sure what you mean for x<-3, isnt the graph restricted to x>=3?
Also the parabola you found, which is the same to mine, passes through D

[bigtick]

x>=-3 is for the cubic, not for the parabola.

[ed_saifa]

I think that a smooth join means the first and second derivatives should be the same.