sketch curve, find intercepts: y = 2x^3 - 9x^2 + 12x - 4

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I need help with this question as I can't seem to get beyong the first step which is finding the intercepts.

Sketch the curve using 5 steps
( the 5 steps are: intercepts, asymptotes, max/min,concavity, sketch)

y= 2x^3 - 9x^2 + 12x - 4

intercepts: 0 = 2x^3 - 9x^2 + 12x - 4

x(2x^2 - 9x + 12) - 4

I did quad formula, cept I got a negative in a square root near the end..so..did I do it right? and also does that mean there is no solution then for the intercept in the brackets? is it only x = 0?

y = -4
x = 0

thanks for the help, if you have time could you please graph it so I can see how to graph it for later, you don't need to show all the 5 steps..
 
Here's the graph.

cubic8gm.jpg
 
to find the x-intercepts (roots) of a cubic by hand, you either have to factor the cubic by grouping or determine any roots using the rational root theorem. the quadratic formula will not work with a cubic equation.

this particular cubic polynomial will not factor by grouping, so you'll have to use the rational root theorem.

if the polynomial has rational roots, they will be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

factors of 4 ... (all +/-) 1, 2, and 4
factors of 2 ... (all +/-) 1 and 2

possible rational roots are (all +/-) 1/2, 1, 2, and 4

try any one of these using synthetic division ... once you find one, finding the other two will be easy by factoring or using the quadratic formula with the depressed quadratic polynomial.

as far as graphing it, you need to complete an analysis using the intercepts and information gained from the first and second derivatives (increasing/decreasing, max/mins, inflection points, etc.) so you may sketch the curve.
 
rational root theorm? hmm I sorta remember learning sometihng with the p/q but I forget how to do it.. you like get the last number in the equation and make it over the first? Or something like that..is there a formula?
 
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