1 - $f(5)=2$ 2 - $f(3)=3$
How to determine the coefficients $a, b ,c$ in the polynomial equation like: $$f(x) = ax^2 + bx + c$$
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Any two points define a straight line so allow $a=0$ the $y=x-8$ is a solution. This also implies an infinite solutions due to the free variable a. For example
$-0.153661 x^2+0.229292 x+5.69508=y$ and $y = 2.84754 + 0.229292 x - 0.307323 x^2$.
Both of the above are generated by adding a third point then calculating. Its a good exercise to see what third points can be added to the parabola with those constraints and why.