Translated
cubic functions |
Drawing graphs of translated
cubic functions |
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Cubic
function
y
=
a3x3
+
a2x2
+
a1x + a0 |
There are three types
(shapes) of cubic
functions whose graphs are shown in the figure below: |
type
1 |
y
=
a3x3
+ a2x2
+ a1x
+ a0
or y
-
y0
= a3(x
-
x0)3,
-
(a2)2
+ 3a3a1
= 0 or a1
= 0. |
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therefore,
its source function y
=
a3x3,
and the tangent line through the point of
inflection is horizontal. |
type
2/1 |
y
=
a3x3
+ a2x2
+ a1x
+ a0
or
y
-
y0
= a3(x
-
x0)3
+
a1(x
-
x0),
where a3a1>
0 |
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whose
slope of the tangent line through the point of inflection is
positive and equals a1. |
type
2/2 |
y
=
a3x3
+ a2x2
+ a1x
+ a0
or
y
-
y0
= a3(x
-
x0)3
+
a1(x
-
x0),
where a3a1<
0 |
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whose
slope of the tangent line through the point of inflection is
negative and is equal a1. |
The
graph of its source function has three zeros or roots at |
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and two turning
points at |
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Translated
cubic functions |
type
1 |
y
=
a3x3
+ a2x2
+ a1x
+ a0 or
y
-
y0
= a3(x
-
x0)3-
x0)3-
x0)3-
x0)3
where, |
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The
root |
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The point of inflection I(x0,
y0). |
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type
2/1 |
y
=
a3x3
+ a2x2
+ a1x
+ a0 or
y
-
y0
= a3(x
-
x0)3
+ a1(x
-
x0),
a3
· a1
>
0, |
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I(x0,
y0). |
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type
2/2 |
y
=
a3x3
+ a2x2
+ a1x
+ a0 or
y
-
y0
= a3(x
-
x0)3
+ a1(x
-
x0),
a3
· a1
<
0, |
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If
| y0
| > |
yT
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if
| y0
| < |
yT
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The turning points |
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The
point of
inflection
I(x0,
y0). |
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