|
|
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|
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| Quartic
function y
=
a4x4
+ a3x3
+
a2x2
+
a1x + a0 |
| Thus,
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4
+
a2(x
-
x0)2
+
a1(x
-
x0), |
 |
 |
| by
setting x0
=
0 and y0
= 0 we get
the source quartic y
=
a4x4
+
a2x2
+
a1x. |
|
|
| By
setting the coefficients a2
and a1
of the source quartic to zero interchangeably, obtained is the
basic classification shown in the diagram. |
 |
| There are
altogether ten types (shapes of the graphs) of quartic functions. |
| The
graphs of the quartic functions
types 1 and 2 |
| type
1 |
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4,
a2
= 0 and a1
=
0. |
|
 |
| The
zeroes or roots: |
 |
|
|
|
|
| type
2 |
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4
+ a1(x
-
x0),
a2
= 0. |
|
 |
| The
zeroes of the source function: |
 |
 |
|
| The
zeroes of the translated function we get
by adding x0
to the solution of the
equation a4x4
+ a1x +
y0
= 0. |
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