Solving Cubic equation to graph

MathTroubled

Homework Statement

Graph this equation:
P=-0.2t^3+2t^2+8t+2
t belongs to [0,13]

The Attempt at a Solution

Can't seem to get factored to find x-int.
and the rest of the graph.

Yep it doesn't factorize nicely. That means you can't easily find the x-intercept(s), but don't let that stop you (there may not even be any x-intercepts in your region of interest).

Go ahead and find the start/end points plus any max/min and POIs in the given region.

MathTroubled
Im kinda math troubled like my username says lol.
Can anyone show me the steps they took to solve this?

Homework Helper
Dearly Missed
Im kinda math troubled like my username says lol.
Can anyone show me the steps they took to solve this?

Have you never, ever, drawn a graph before?

RGV

MathTroubled
yeah my textbook doesn't describe transformations well for this chapter.

Homework Helper
Dearly Missed
yeah my textbook doesn't describe transformations well for this chapter.

If you have already done similar things before, just do the same things for this problem.

If you have not drawn a graph before (and if your book does not explain how to do it) there are numerous web pages
that explain what to do. For example, see
http://cstl.syr.edu/fipse/grapha/unit2/unit2.html [Broken] and
http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i14/bk8_14i3.htm .
In your case, however, the curve y = f(t) is not a straight line, so all you can do is make a table of some(t,y) values, and
hand-draw a smooth curve that passes through them.

RGV

Last edited by a moderator:
Homework Helper
Plot a graph of p vs t for some values of t in your range of interest.
Stand back and look what shape it is trying to be and where it seems to be heading for the t axis. This will tell you when you are getting close to the roots.

Particularly - plot p for t=0 and t=13 (your endpoints). If your endpoints are on opposite sides of the t axis, then there is at least one root. If p is on opposite sides of the t axis for two adjacent values of t, then there is at least one root between them.

Use Newton-Raphson's method to get the rest of the way.

Looks like you can find and characterize the turning points of the graph OK ... that will also give you clues.

Or you can look up the general formula:
http://en.wikipedia.org/wiki/Cubic_function

Staff Emeritus
Homework Helper
Gold Member

Homework Statement

Graph this equation:
P=-0.2t^3+2t^2+8t+2
t belongs to [0,13]

The Attempt at a Solution

Can't seem to get factored to find x-int.
and the rest of the graph.
If you shift the graph down by 2 you can factor that.

y = P(t) - 2 = -0.2t3+2t2+8t .