How can I make a printable list with different quadratic functions and with points that belong or not to them so that a young person can check whether or not the point belongs to the parabola? my code is horrible (I can't get it not to take the number zero)

something like the image

sig := 2*Random[Integer, {0, 1}] - 1;
a := Random[Integer, {-9, 9}];
b := Random[Integer, {-9, 9}];
c := Random[Integer, {-9, 9}]
nul := Random[Integer, {0, 1}] - 1;

For[i = 1, i <= 30, i++, 

Print[i, " f(x) = ", siga, "x^2", nulsigb, "x ", nulsig*c]]

How can I make a printable list with different quadratic functions and with points that belong or not to them so that a young person can check whether or not the point belongs to the parabola? my code is horrible (I can't get it not to take the number zero)

something like the image

sig := 2*Random[Integer, {0, 1}] - 1;
a := Random[Integer, {-9, 9}];
b := Random[Integer, {-9, 9}];
c := Random[Integer, {-9, 9}]
nul := Random[Integer, {0, 1}] - 1;

For[i = 1, i <= 30, i++, 
 Print[i, " f(x) = ", sig*a, "x^2", nul*sig*b, "x ", nul*sig*c]]