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#1 2009-08-17 16:27:16
- Greaterpathmagician
- Member
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Finding the quadratic equation
Hello
I don't know how to find the quadratic equation from a table of values.
Here is the question and some of the tables of values.
Question: For those that are one of the above five types determine the algebraic rule for the reationship in the form of "y=???'.
("udef" indicates that the function is undefined for that value of x)
a) x: -4, -3, -2, -1, 0, 1, 2, 3, 4
y: 12, 6, 2, 0, 0, 2, 6, 12, 20
b) x: -4, -3, -2, -1, 0, 1, 2, 3, 4
y: 6, 2, 0, 0, 2, 6, 12, 20, 30
I know how to identify if it is quadratic (i.e the second difference) but not how to find and write the equation.
Thank you
Last edited by Greaterpathmagician (2009-08-17 16:29:30)
#2 2009-08-17 16:39:42
- bobbym
- Administrator
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Re: Finding the quadratic equation
Hi Greaterpathmagician;
a) y=x^2+x
b) y= x^2+3x+2
These were found by interpolation and there are other ways.
Last edited by bobbym (2009-08-17 16:44:20)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2009-08-17 21:27:48
- mathsyperson
- Moderator
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Re: Finding the quadratic equation
Second difference is one way to do it.
6, 2, 0, 0, 2, 6, 12, 20, 30
-4, -2, 0, 2, 4, 6, 8, 10
2, 2, 2, 2, 2, 2, 2
The second difference is 2, and dividing that by 2 gets you the coefficient of the quadratic term.
So now you know that the equation will be x², plus a linear part.
One way of finding the linear part is to take x² away from the terms in the sequence and analyse what's left.
-10, -7, -4, -1, 2, 5, 8, 11, 14
Why did the vector cross the road?
It wanted to be normal.