WOLFRAM|DEMONSTRATIONS PROJECT

Parameters for Plotting a Cubic Polynomial

​
parameters:
point of inflection
x
N
2
point of inflection
y
N
1
height h
-0.4
width δ
0.5
plot range:
dx
2
dy
2
cubic coefficients:
a
3
=
1.6
a
2
=
-9.6
a
1
=
18.
a
0
=
-9.4
​
​
​
slope
m
N
=
-1.2
A cubic polynomial
f(x)=
a
3
3
x
+
a
2
2
x
+
a
1
x+
a
0
is normally characterized by the coefficients
a
3
,
a
2
,
a
1
,
a
0
.
However, these coefficients are not well suited to describe the geometrical shape of the graph of the cubic. Nickalls found a set of parameters
(
x
N
,
y
N
,h,δ)
that do a better job. The relation between the parameter sets is given in the Details section.
The parameters
(dx,dy)
define the plot range
x
N
-dx≤x≤
x
N
+dx
and
y
N
-dy≤y≤
y
N
+dy
.