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Translated
cubic functions |
Translated
cubic function, the type 1 - the tangent line at the point of
inflection is horizontal |
Translated
cubic function, the type 2/1 - no turning points, the tangent at
inflection is a slant line |
Translated
cubic function, the type 2/2 - with two turning points, the
tangent at inflection is a slant line |
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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
where, |
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![](CubicType1.gif) |
![](CubicGraphT1.gif) |
The
root |
![](CubicT1Root.gif) |
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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![](CubX0Y0.gif) |
![](CubicGraphT21.gif) |
![](CubRootT21.gif) |
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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![](CubX0Y0.gif) |
![](CubicGraphT22.gif) |
If
| y0
| > | yT
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![](CubRootT21.gif) |
if
| y0
| £
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yT
| |
![](CubRootsT22.gif) |
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![](CubRootsT22A.gif) |
The turning points |
![](CubT22TPts.gif) |
The
point of
inflection
I
(x0,
y0). |
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Pre-calculus contents
E |
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