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Any equation where variable a = some multiple of variable b2 + constant will graph a parabola.
Almost every graph shows some relationship. The relationship may besimple or complicated,linear, quadratic or more complicated,one-to-one or one-to-many,exact or approximate.
In a velocity-time graph it will be the time axis (where velocity = 0). On a distance-time graph it will be a line parallel to the time axis: distance = some constant (which may be 0).
The nature of displacement-time graph is parabolic if the acceleration is constant(uniform). When acceleration is constant, displacement is directly proportional to the square of time which results into a parabolic structure of graph.
The word graph can be used either as a noun or a verb. As a noun, it means a picture or visualization of some mathematical term or relationship. The most usual type of graph is the Cartesian coordinate system invented by the great French mathematician, René Descartes, but there are several other types. As a verb, to graph is to depict in the form of a graph, as in, graph that equation.