The Parabola. Example2

Finding the Parabola y = a x^2 + b x + c

Let's call the parabola P
> P := y = a*x^2 + b*x + c:

When x = -1 then y = 6

> E1 := subs({x=-1, y=6}, P);

                              E1 := 6 = a - b + c

When x = 1 then y = 4

> E2 := subs({x=1, y=4}, P);
                               E2 := 4 = a + b + c

When x=2 then y=9

> E3 := subs({x=2, y=9}, P);
                            E3 := 9 = 4 a + 2 b + c

This is a system of three linear equations in the three unknowns a, b, c. The solution is given by

> solve({E1, E2, E3}, {a,b,c});

                             {c = 3, b = -1, a = 2}