Sketching a cubic?!! (1 Viewer)

[Jinxd]

y = 2x^3 - 9x^2 + 12

I've found the stationary pts to be:
MAX (0,12) MIN (3,-15)

BUT I don't know how to find the x-intercepts. Usually, I would make y=0 then solve the polynomial, but in this case, i can't factorise it.

so, can someone help me find the x-intercepts? and tell me how, plz.

ty

 

[Morgues]

in 2 unit you dont really need to specify where it crosses the x axis..............they are just looking for a general sketch of the curve

 

[Jinxd]

That's good to know, but what about 3U? Would they ask for the x-int? If so, I'd still need an answer.

 

[Morgues]

in 3 unit if you really wanted it you could use the factor theorem and long division, or zeroes to factorise it.......but unless the question specifically asked for it or you had a lot of time to waste i wouldnt bother

 

[Morgues]

isnt he asking about where a graph crosses the x axis?

 

[Jinxd]

Ahhh, yes. Pt of Inflexion, but that would be 1 of the 3 points. How would you find the ones on the side?

Btw, ty for all the replies

 

[Jinxd]

Nope, they didn't give a domain. I guess i don't need to do that much.

 

[Lazarus]

You don't need to mark in the x-coordinates for any curves of degree 3 or higher, unless the question specifically states otherwise, in which case - if it's a difficult polynomial - use Newton's method or the halving the interval method to approximate the roots.

You won't even be asked to do that much in 2u.

 

[bos1234]

How about using the theorem

i forogt how it goes but the numerator is a factor of the constant

denom. is a factor of leading coefficient

is this therom 4 unit or 3 unit?

 

[pLuvia]

You can just use calculus to draw a cubic curve

I'm not sure what theorem you are talking about, but this thread is 4 years old

 

[buchanan]

You could use the <a href="http://users.tpg.com.au/nanahcub/cubic.gif">cubic formula</a> to do it and you get three real roots:

 

[Danitel]

I dont think you need to do this in 2U.....

And I cant even remember the 4U required to find the exact graph of the cubic equation...

Just need to find out the stationary points and inflextion points to sketch the graph out....

As you know the max and min points, and also the inflextion points, you can sketch the graph easily....

 

[buchanan]

y = 2x^3 - 9x^2 + 12

I don't know how to find the x-intercepts.

can someone help me find the x-intercepts?

and tell me how, plz.

I dont think you need to do this

I answered Jinxd's question, not an HSC question.

I actually don't usually provide answers to students questions online - unless it's interesting.

Most HSC questions are boring. In fact, the main problem with the current syllabus is that it's boring!

Jinxd's question however is interesting, as is my answer.