Q&A #758

Graph of a cubic equation

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 09, 1998 at 16:39:48
Subject: Graph of a cubic equation

Hi, Toon,

No, I cannot draw a graph of a cubic equation, because I do not have the
capability with this email software.  However, I think that if I describe a
cubic equation's graph, you might be able to draw one.

Take the following coordinates and locate them on a grid.  (-4, -12)   (-3,0)
(-2, 4), (-1,3), (0,0) (1, -4) (2,0)  (3, 9).   Starting on the left side of
the grid draw a line that passes through all of these points in sequence as
you go from left to right.   You will notice that the graph has a high point
(or mountain) followed by a deep valley followed by a rise up again.   Every
graph of a cubic equation has a high point and a valley or is shaped
like an s-shaped curve.  If you have access to a graphing calculator or a
computer, graph:  y = .5x(x+3)(x-2).   Also graph y = x(x+1)(x-1)  as well as
y=.5x^3.   All of these are cubics.

 -Marielouise, for the Teacher2Teacher service

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