SOLUTION: How do you get the quadratic equation if you are given a table of values?

Question 567835: How do you get the quadratic equation if you are given a table of values?
Answer by issacodegard(60) (Show Source): You can put this solution on YOUR website!
You must be given at least 3 points, call them (x1,y1),(x2,y2),(x3,y3). Then we know the equation has the form f(x)=ax^2+bx+c. We get a system of 3 equations in 3 unknowns. Solving for a,b,c in,

gives you the equation for f(x).
I'll give an example,
If we know that three points are (-1,-2),(1,4),(2,13). Then we set up three equations about a,b,c that we know:

So we have,

We need to solve for a,b,c. So, we subtract eqn1 from eqn2 to get,

Divide eqn2 by 2 to get b=3. Then, we have

So,

Subtract the first eqn from the second to get,

Divide the second eqn by 3 to get a=2. Then we have

So,

Therefore we find that

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