A cubic duty is one in the type f ( x ) = a x 3 + b x 2 + c x + d .

The "basic" cubic function, f ( x ) = x 3 , is graphed below.

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The role of the coefficient a in the basic equation is to do the graph "wider" or "skinnier", or to reflect that (if negative):

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The consistent d in the equation is the y -intercept that the graph.

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The effects of b and c on the graph are much more complicated. However, if you deserve to variable the right side the the equation, girlfriend can find one or much more x -intercepts , and use this to map out the graph. (Some cubics, however, can not be factored.)

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A cubic duty may have actually one, 2 or 3 x -intercepts, corresponding to the actual roots of the associated cubic equation.


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