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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
Subtract the first eqn from the second to get,
Divide the second eqn by 3 to get a=2. Then we have
Therefore we find that