VCE Methods Question Thread!

[brightsky]

you 'can't', unless more information is known about the points (e.g. one of them is a stationary point, etc.). there will be infinitely many cubics which satisfy the given condition. in general, you need 2 points to find the equation of a line, 3 points to find the equation of a quadratic, and 4 points to find the eqaution of a cubic.

[Daenerys Targaryen]

If given 3 points of a cubic, how do you find the original equation?

i.e. a cubic equation passes through the points (0,6) (-1,12) (2,12)

you 'can't', unless more information is known about the points (e.g. one of them is a stationary point, etc.). there will be infinitely many cubics which satisfy the given condition. in general, you need 2 points to find the equation of a line, 3 points to find the equation of a quadratic, and 4 points to find the eqaution of a cubic.

Unless one of these points are a stationary point you won't be able to.
Does the question say?

[Homer]

i actually thought you could i get where -x^3+7x^2-11x+6

[abcdqdxD]

Ahh my bad, I just made the question up on the spot.

How would you work out the equation of (0,-2) (0.75,-3.125) (3,7)

So to get the equation of a cubic you require either 4 points or 3 points including a y intercept and stationery point?

[Jeggz]

Yeah exactly  So if you can use your calculator then cubic regression is the way to go, however if it is a non-cas question then you would substitute each of the points which you are given and you will then be required to solve those equations simultaneously in order to find out the equation of the quadratic. Using the general formula is often the best approach, unless you are given an x-intercept or a stationary point!

[abcdqdxD]

ahh ok cheers. could someone show me how to solve it simultaneously? (sorry I know it's a pain to type but I've never done this type of question by hand)

[abcdqdxD]

how is a cubic regression done on the casio classpad? when I go to stats and enter the three coordinates then click cubic reg it says stat "error! stat calculation"

[Jeggz]

how is a cubic regression done on the casio classpad? when I go to stats and enter the three coordinates then click cubic reg it says stat "error! stat calculation"

You need four points for a cubic regression 

[abcdqdxD]

If I've only got 3 points how do I do it on the calculator?

[Professor Polonsky]

Since there are four unknowns in a cubic (), you must have four different points to find the equation.

[abcdqdxD]

even if the stationery point is given?

[shadows]

Just bored and did a random question for teh lolz....
So I haven't solved quadratic equations by completing the square for a LONG time...
I've encountered a question and tried to do it by C.T.S

Hmm I've so (x^2+3x+9)

= (x+3/2)^2 - (27/4)

I put it in the format by combining these two into two factors by taking the square root of (27/4) and adding and subtracting from (x+3/2) ... To create to factors

I put it in the calc and expanded it to check but it turned out to be x^2+3x+(9/2)

LOL WUT? I havent done CTS for long long time... just wondering if theres something I did wrong. Or maybe theres an error on the calc..

I remember doing this method years ago... and it worked.. unless my brains retarded and i forgot something majorly important.. Thanks xD

[Lasercookie]

Hmm I've so (x^2+3x+9)
= (x+3/2)^2 - (27/4)

Looks like you mucked up your negatives and positives when computing

will expand out to

[shadows]

OMFG HAHAHA  im soo clumsy..

thanks though

[BubbleWrapMan]

even if the stationery point is given?

If there's a stationary point at, say, x = p, you'd use f'(p) = 0 to generate a fourth equation.