|
|
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 |
|
|
|
|
|
|
|
| Translated
cubic functions |
| type
1 |
y
=
a3x3
+ a2x2
+ a1x
+ a0 or
y
-
y0
= a3(x
-
x0)3-
x0)3-
x0)3
where, |
|
 |
 |
|
The
root |
 |
The point of inflection I
(x0,
y0). |
|
|
|
|
| type
2/1 |
y
=
a3x3
+ a2x2
+ a1x
+ a0 or
y
-
y0
= a3(x
-
x0)3
+ a1(x
-
x0),
a3
· a1
>
0, |
|
 |
 |
 |
I
(x0,
y0). |
|
|
|
|
| type
2/2 |
y
=
a3x3
+ a2x2
+ a1x
+ a0 or
y
-
y0
= a3(x
-
x0)3
+ a1(x
-
x0),
a3
· a1
<
0, |
|
|
 |
| If
| y0
| > | yT
| |
|
| if
| y0
| £
|
yT
| |
 |
|
 |
|
The turning points |
 |
The
point of
inflection
I
(x0,
y0). |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Pre-calculus contents
E |
|
|
 |
|
| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
|
|
