Math Is Fun Forum

SmellyMan

Guest

Equations with 3 variables.

I have a little problem of my own, now I just want to see if I am doing it correctly, since I do not have the right answer at my disposal .

Ok so we have 3 points:

A(1,-6)
B(-1,0)
C(2,-24)

So we use the basic form:
f(x)=ax^2+bx+c

And insert those points to come up with 3 different equations:

-6=a+b+c
0=a-b+c
-24=4a+2b+c

In order to get rid of the 2 variables we multiply the first one with (-1).

6=-a-b-c

And by 'joining' the first and the second one we get:

6=-2b

b=-3

Now that we have b, we need a or c. I decided to go for a.
-18=3a+b

Inserting the b, we get:

a=-5

All good and clear for now, we just have to get c.

I'll insert the variables here:
0=a-b+c

0=-5+3+c

2=c

So we have these three variables:

a=-5
b=-3
c=2

Now we just write the function:
f(x)=-5x^2-3x+2

Is this correct?

I also know this is one of the easiest, and if I took anything complicated I would probably be left of with equations with 2 variables.

Thank you and enjoy the rest of your day/night ^^.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equations with 3 variables.

Hi SmellyMan;

Welcome to the forum!

That is the correct interpolating polynomial fit. That is also the generic way to do all of them and a lot more. As long as you have the same number of equations as you have variables and the equations are linear independent you will always be able to find the answer in just that way.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.