We call this shapea parabolaand everyquadraticfunction, has a parabola-
shapedgraph.Let’s recallhow we analyticallyfind the key pointson the parabola.The vertexwill be the
lowestpoint,. In general,the vertexis locatedat the point. We then can
identifypointscrossingthe and axes.Theseare calledthe interceptsof the equation.The -intercept
is foundby setting in the equation,and then solvingfor as follows:
The -interceptis locatedatThe -interceptis foundby setting in the equation,and solvingfor as follows:
Usingthe quadraticformula,we find that. The -interceptsare locatedat
and.
Finally, recallthat we definedthe symmetryof a graph.We notedexamplesof verticaland horizontalline
symmetryas well as symmetryaboutparticularpoints.For the currentexample,we note that the graphhas
symmetryin the verticalline The graphwith all of its key characteristicsis summarizedbelow: