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The
graphs of the quartic function
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The
basic classification diagram for the quartic polynomial function |
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| The
transition of quartic function
expression |
| Thus,
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4
+
a2(x
-
x0)2
+
a1(x
-
x0), |
 |
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| by
setting x0
=
0 and y0
= 0 we get
the source quartic y
=
a4x4
+
a2x2
+
a1x. |
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| The
basic classification diagram for the quartic polynomial function |
| By
setting the coefficients a2
and a1
of the source quartic to zero, interchangeably, obtained is the
basic classification shown in the diagram. |
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| There are
ten types (shapes of the graphs) of quartic functions. |
| type
1 |
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4,
a2
= 0 and a1
=
0. |
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| The
zeroes or roots: |
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| type
2 |
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4
+ a1(x
-
x0),
a2
= 0. |
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| The
zeroes of the source function: |
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| 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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| type
3 |
y
= a4x4
+ a3x3
+
a2x2
+
a1x + a0
or y
-
y0
=
a4(x
-
x0)4
+ a2(x
-
x0)2,
a1
= 0. |
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T
(x0,
y0). |
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| Pre-calculus contents
D |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
