How do you find the quadratic coefficient a, b, and c, given some values of x and y?
For example: Suppose we have
f(0.1524)=0.9961
f(0.8258)=0.0782
f(0.5383)=0.4427
and given the quadratic equation: $y = ax^2 + bx + c$, then can you find values of x and y?
Is there a formula to find these a, b, and c? when I think about the general formula, but in this case y=0. So, it does't work. When I think about substitute by the formula: $y = ax^2 + bx + c$, I cannot get go long; because we have three unknown in one equation. So, what you suggest as next step.
Thank you!
Best Answer
If you are given $3$ points with distinct $x$ values, by substituting those values inside $y=ax^2+bx+c$, we can obtain $3$ linear equations in terms of $a, b$, and $c$.
Hence, the problem reduces to the problem of solving a linear system of equations, which can be solved, for example, by Gaussian elimination.