Determining the Equation of a Quadratic From a Graph

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Every quadratic graph is unique, since if two quadratic graphspass through the same set of points, they must be the same graph. Thegeneral equation of a quadratic graph is(1).This has three constantsandsowe can use three points on the graph to write down three simultaneousequations and solve them to findand

Example: The graph below passes through the p[ointsand

Substitute these points into the equation (1) to give thesimultaneous equations

(2)

(3)

(4)

Substitutinginto(3) and (4) gives

(5)

(6)

(6)-2*(5) gives

From (5) then