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Determining the Equation of a Quadratic From a Graph

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 constantsandso 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[ointsand

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

(2)

(3)

(4)

Substitutinginto (3) and (4) gives

(5)

(6)

(6)-2*(5) gives

From (5) then