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**lakitu****Member**- Registered: 2006-03-08
- Posts: 5

hi apologise if this is in the wrong forum

my lecturer has told me that i need to be able to express parametric equations as a cartesian equation and then Simplify it into the form y = a x² + b x + c in my exam later this month. my mind boggles !

here is an example i have found.

Express the parametric equations x = t + 1 and y = -3 t² + 3 t as a Cartesian equation in just x and y.

any help would be great!

kind regards lakitu

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**lakitu****Member**- Registered: 2006-03-08
- Posts: 5

hi again, i have re written my question in a better way, sorry for the confusion.

i have figured out how to do a simple parametric - cartesian equation in the form of x and y here is what i have already done.

x = 2 t - 2 -----------------(1)

y = 3 t - 2 -----------------(2)

multiply (1) by 3 and (2) by 2.

3x = 6 t - 6 -----------------(3)

2y = 6 t - 4 -----------------(4)

eliminate t from the two eqns by subtracting (4) from (3)

3x - 2y = -6 + 4

3x - 2y = -2

in my exam i am assured i will need to know harder ones like this, but i cannot figure out how to do these.

Express the parametric equations x = t + 1 and y = -3 t² + 3 t as a Cartesian equation in just x and y.

i also need to simpify this in the form y = a x² + b x + c.

Any help would be great.

kind regards lakitu

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,998

Since x=t+1, t=x-1.

Given

y=-3t²+3t

Therefore,

y=-3t(t+1)+6t

y=-3(x-1)(x)+6(x-1)

y=-3x²+3x+6x-6

y=-3x²+9x-6.

You can verify this by substituting x=t+1 in the Cartesian equation.

y=-3(t+1)²+9(t+1)-6

y=-3t²-6t-3+9t+9-6

y=-3t²+3t

This is the parametric equation of y given.

Hence, the Cartesian equation is correct.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

If x = t+1, then rearranging gives t = x-1

We can then substitute (x-1) for t in the equation y = -3t² + 3t so that:

y = -3(x-1)² + 3(x-1)

Multiply out to give:

y = -3(x²-2x+1) + 3x -3

and further to give:

y = -3x² +6x -3 + 3x -3 = -3x² + 9x - 6

Factorising -3x² + 9x - 6 gives:

y = (-3x + 3)(x-2) OR -3(x-1)(x-2)

Solving for y=0 gives x= 1 or 2

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

Shucks! Beaten to it by 5 seconds!!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Hehe, don't worry, it happens to all of us. I was beaten by 3 seconds not too long ago.

But eventually, you're going to beat someone by a tiny amount as well, and the universe will be restored.

Why did the vector cross the road?

It wanted to be normal.

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

mathsy, calculate the following:

What is the probability that ashwil will not only be able to answer an algebra/calculus question correctly, but will also be able to type & post his answer before ganesh, Ricky, krassi_holmz, yourself, mathisfun etc etc.?

I want my mummy!

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**lakitu****Member**- Registered: 2006-03-08
- Posts: 5

thank you to both of you ! big help i understand it all

regards

lakitu

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

for ashwil:

the probability is 5 seconds less than ganesh's.

IPBLE: Increasing Performance By Lowering Expectations.

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