Every quadratic graph is unique, since if two quadratic graphs pass through the same set of points, they must be the same graph. The general equation of a quadratic graph is
(1). This has three constants
and
so we can use three points on the graph to write down three simultaneous equations and solve them to findand
Example: The graph below passes through the p[oints
and
Substitute these points into the equation (1) to give the simultaneous equations
(2)
(3)
(4)
Substituting
into (3) and (4) gives
(5)
(6)
(6)-2*(5) gives
From (5) then