## mikaa_toxica13 2 years ago fan and medal awarded Graph y = x^3 – 2x^2 + 6. Describe what you see.

1. heathernelly

type online graphing calculator on google and chose the first one that says holt mcdougal

2. heathernelly

then just type it in! :D

3. mikaa_toxica13

my pc will lag. so i cant. can u jus help me ??

4. mikaa_toxica13

@tcarroll010 can u help

5. tcarroll010

ok, I got a hold of the older version. It looks like:

6. heathernelly

yeah, that's what it looks like

7. mikaa_toxica13

i need it described

8. tcarroll010

You can see how it has a local maximum at x=0 and a local minimum at around x = 1.something and how it goes off to positive infinity as x gets larger and it goes to negative infinity as x gets smaller.

9. tcarroll010

Are you in calculus?

10. mikaa_toxica13

no thank god.

11. tcarroll010

If you are in calculus, if you take the first degree derivative, then you would see that the local minimum is at x= 4/3. It's good to know that that local minimum is at x= 4/3 even if you are not in calculus. Also, for further description, it has a y-intercept at (0, 6). We could try to see if the x-intercept is a rational zero.

12. tcarroll010

ok, other things that might help you: we already covered that the local max is at (0, 6) and that is of course the y-intercept. The x-intercept is irrational (the x value for which the function equals "0") but it is approximately (-3/2, 0). We already described the end behaviors. The only last thing to say is squarely in the realm of calculus where the graph is "concave down" between x = negative infinity to 2/3 and it is "concave up" between x = 2/3 to positive infinity. "concave up" means that the graph looks like a "bowl" right-side up in that interval. "Concave down" is an inverted bowl. Hope this all helps. When I learned calculus a thousand years ago, this was the extent of everything we needed to know to graph, and we were able to graph these functions by hand with no computer, so since you are in algebra or algebra II, this really should be all you need I would think.