Hi I need some info on how to Sketch the square of functions.
Eg (x+6)(x+3)(x-4) Sketch the square and comment on the number of turning points.
Can someone find a website on this? I have searched google to no avail.
Thanks
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Hi I need some info on how to Sketch the square of functions.
Eg (x+6)(x+3)(x-4) Sketch the square and comment on the number of turning points.
Can someone find a website on this? I have searched google to no avail.
Thanks
The functionQuote:
Originally Posted by classicstrings
is always greater than or
equal to zero, it is increasing as, and touches the
axis when
and
.
Each of the zeros is a turning point, so it must have an additional turning points
between them making at least 5 turning points. Also it can have at most
five turning points (asis a quintic and so has five zeros
which are potential turning points), hence it has exactly 5 turning points.
This should be sufficient to allow you to sketch the curve.
RonL
Hello, classicstrings!
An interesting problem . . . I've never been asked to do this.
Quote:
Sketch the square and comment on the number of turning points.
is a cubic with x-intercepts: -6, -3, 4.
There are two turning points.Code:|
| *
|
** | *
-6 * * | *
- - o - + - + - o - + - + - + - + - + - o - - -
* -3* | * 4
* | *
* *| *
| **
|
has the same x-intercepts but of order two.
. . The graph is tangent to the x-axis there.
Also the entire graph is above (or on) the x-axis.There are five turnning points.Code:|
* | ** *
** |* *
* * * *| * *
* * * * | * *
- - o*- + - + - o*- + - + - + - + - + -*o - - -
-6 -3 | 4
Thanks for your help guys! The diagrams + explanations rock! CHeers!!!
EDIT: If you read what i posted before forget it!
EDIT: Soroban do you post on other maths help boards? I think I have seen you elsewhere.
Also where would the intercepts of the two lines be? Thanks